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Recent questions and answers in Linear Algebra
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ISIMMA201544
Let $P_{1},P_{2},$ and $P_{3}$ denote, respectively, the planes defined by $a_{1}x + b_{1}y + c_{1}z = \alpha _{1}$ $a_{2}x + b_{2}y + c_{2}z = \alpha _{2}$ $a_{3}x + b_{3}y + c_{3}z = \alpha _{3}$ It is given ... then the planes (A) do not have any common point of intersection (B) intersect at a unique point (C) intersect along a straight line (D) intersect along a plane
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Linear AlgebraMETest
If the determinant of the below matrix is 245, what is the value of X? $\begin{bmatrix} 0 & 4& 2 &1 \\ 3& 1 & 0 & 2\\ 5&2 & x& 4\\ 6& 1 & 1 & 0 \end{bmatrix}$ ... , because by keeping 6 in place of x I am getting determinant as 245(Result verified by computer program). Please let me know where I am going wrong?
answered
4 days
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Linear Algebra
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Meet2698
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133
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+20
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4
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3
GATE2015227
Perform the following operations on the matrix $\begin{bmatrix} 3 & 4 & 45 \\ 7 & 9 & 105 \\ 13 & 2 & 195 \end{bmatrix}$ Add the third row to the second row Subtract the third column from the first column. The determinant of the resultant matrix is _____.
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Ram Swaroop
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gate20152
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+14
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3
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4
GATE19982.1
The rank of the matrix given below is: $\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &2 \end{bmatrix}$ $3$ $1$ $2$ $4$
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gate1998
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+4
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3
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5
ISRODEC201717
If $C$ is a skewsymmetric matrix of order $n$ and $X$ is $n\times 1$ column matrix, then $X{^T} CX$ is a scalar matrix null matrix unit matrix matrix will all elements $1$
answered
Feb 12
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Linear Algebra
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Abhisek Tiwari 4
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isrodec2017
matrices
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3
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6
GATE20199
Let $X$ be a square matrix. Consider the following two statements on $X$. $X$ is invertible Determinant of $X$ is nonzero Which one of the following is TRUE? I implies II; II does not imply I II implies I; I does not imply II I does not imply II; II does not imply I I and II are equivalent statements
answered
Feb 7
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Linear Algebra
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Sukhbir Singh
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309
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1.5k
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gate2019
engineeringmathematics
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determinant
+2
votes
3
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7
GATE201944
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______
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Feb 7
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Linear Algebra
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Lakshman Patel RJIT
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gate2019
numericalanswers
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linearalgebra
eigenvalue
+21
votes
2
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8
GATE2015118
In the LU decomposition of the matrix $\begin{bmatrix}2 & 2 \\ 4 & 9\end{bmatrix}$, if the diagonal elements of $U$ are both $1$, then the lower diagonal entry $l_{22}$ of $L$ is_________________.
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Feb 6
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Linear Algebra
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Verma Ashish
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gate20151
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9
Previous gate
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Jan 31
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Hemanth_13
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65
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eigenvalue
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10
#math
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Jan 30
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amit166
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693
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19
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engineeringmathematics
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11
ace test series
how? please explain
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Jan 28
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Linear Algebra
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Vignaneswarkrishna
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167
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36
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0
votes
1
answer
12
Gatebook Test
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Jan 28
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Linear Algebra
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Meet2698
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133
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45
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0
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1
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13
Ace test series
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Jan 27
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Linear Algebra
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Meet2698
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133
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55
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acetestseries
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14
Gate 2016 ee
Question number 249
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Jan 27
in
Linear Algebra
by
Vignaneswarkrishna
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167
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25
views
+14
votes
3
answers
15
GATE2004IT36
If matrix $X = \begin{bmatrix} a & 1 \\ a^2+a1 & 1a \end{bmatrix}$ and $X^2  X + I = O$ ($I$ is the identity matrix and $O$ is the zero matrix), then the inverse of $X$ is $\begin{bmatrix} 1a &1 \\ a^2& a \end{bmatrix}$ ... $\begin{bmatrix} a &1 \\ a^2+a1& 1a \end{bmatrix}$ $\begin{bmatrix} a^2a+1 &a \\ 1& 1a \end{bmatrix}$
answered
Jan 27
in
Linear Algebra
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dsomnath
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69
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gate2004it
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+3
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3
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16
Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
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Jan 27
in
Linear Algebra
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askeshavas
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157
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eigenvalue
+30
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6
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17
GATE2007IT2
Let A be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of xT Ax where the maximum is taken over all x that are the unit eigenvectors of A? $3$ $\frac{(5 + √5)}{2}$ $3$ $\frac{(5  √5)}{2}$
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Jan 26
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Sambhrant Maurya
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gate2007it
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18
Nullity of matrix
Nullity of a matrix = Total number columns – Rank of that matrix By how to calculate value of x when nullity is already given(1 in this case)
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Jan 24
in
Linear Algebra
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Somoshree Datta 5
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rankofmatrix
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19
acetest series
asked
Jan 21
in
Linear Algebra
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Rajesh Panwar
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601
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46
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0
votes
1
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20
Made Easy Workbook
Let A be a 3*3 matrix whose characteristics roots are 3,2,1. If $B=A^2A$ then B=? a)24 b)2 c)12 d)12 Please explain in detail.
answered
Jan 20
in
Linear Algebra
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Rishabh Agrawal
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953
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linearalgebra
matrix
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1
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21
Simple Determinant
how to prove determinant 1 and 2 are same by some rowcolumn manipulation ,please Help??
answered
Jan 20
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Linear Algebra
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Rishabh Agrawal
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953
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36
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linearalgebra
engineeringmathematics
matrices
+16
votes
4
answers
22
GATE201826
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the following options ... and III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true
answered
Jan 19
in
Linear Algebra
by
dnivara
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37
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4.8k
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gate2018
linearalgebra
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votes
1
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23
Made easy
answered
Jan 17
in
Linear Algebra
by
kd.....
Junior
(
851
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43
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linearalgebra
madeeasytestseries
0
votes
0
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24
uppcl2018
need soln
[closed]
asked
Jan 11
in
Linear Algebra
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SAUMYA2019
(
97
points)

20
views
0
votes
1
answer
25
GATEBOOK2019 Grand Test Mathematics10
Consider the system of equation $2x+3y+5z = 30 \\ 4x+6y+10z =40 \\ x+y z = 2 $ The above system has No solution a unique solution More than one but finite solutions an infinite number of solutions
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Jan 11
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pranay562
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gb2019gtmaths
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26
made easy
The probability of a man hitting a target in one fire is 1/4 The number of times at least he must fire at the target in order that his chance of hitting the target at least once will exceed 2/3 will be _______.
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Jan 7
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Linear Algebra
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pream sagar
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40
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27
made easy
If 2, – 4 are the eigen values of a nonsingular matrix A and A = –8, then the eigen values of Adj A are x and –y then the value of x + y is _________.
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Jan 7
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Linear Algebra
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pream sagar
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62
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28
Doubt on syllabus
Is LU decomposition in course for GATE 2019?
[closed]
asked
Jan 6
in
Linear Algebra
by
subho16
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149
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38
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engineeringmathematics
ludecomposition
linearalgebra
0
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0
answers
29
GATE 2008 C.E.
The eigen values of the matrix [P] = 4 5 are? 2 5 The answer for this is 6 and 5. My question is what wrong am I doing by R1 = R1 + R2 and converting it to lower triangular matrix. Answer after this is +6 and 5 i.e. sign of eigen values inverted.
asked
Jan 6
in
Linear Algebra
by
Barney Ross
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235
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32
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0
votes
0
answers
30
UPPCL AE 2018:58
asked
Jan 5
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Linear Algebra
by
Lakshman Patel RJIT
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(
29k
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22
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uppcl2018
+18
votes
2
answers
31
GATE201434
Which one of the following statements is TRUE about every $n \times n$ matrix with only real eigenvalues? If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative. If the ... its eigenvalues are positive. If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.
answered
Jan 5
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Linear Algebra
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Parth Shah
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597
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2k
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gate20143
linearalgebra
eigenvalue
normal
0
votes
0
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32
Eigen Values Doubt
Let there is a 2*2 Matrix and their eigen values are A and B. The eigen values of $(A+7I)^{1}$ ?
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Jan 4
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Linear Algebra
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Shamim Ahmed
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73
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eigenvalue
engineeringmathematics
linearalgebra
0
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33
Gatebook Test
[closed]
asked
Jan 4
in
Linear Algebra
by
Shadan Karim
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979
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70
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+1
vote
0
answers
34
Gatebook Test
asked
Jan 4
in
Linear Algebra
by
Shadan Karim
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979
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73
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0
votes
0
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35
Gatebook Test
asked
Jan 4
in
Linear Algebra
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Shadan Karim
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979
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32
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+1
vote
0
answers
36
Gatebook Test
asked
Jan 4
in
Linear Algebra
by
Shadan Karim
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979
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32
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+1
vote
0
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37
rc test series
If A=$\begin{bmatrix} 1 & 2\\ 1& 3 \end{bmatrix}$ then $\ A^{6} 4A^{5}+8A^{4}12A^{3}+14A^{2}$=? a)0 b)4A c)4A+5I d)4A+5I am gettind d
asked
Jan 3
in
Linear Algebra
by
Gate Fever
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54
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votes
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38
GEEKS 4 GEEKS  gate cs mock 2018
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix ? 7/4 1/7 7 4/7 Answer given : 7/4 My answer : 7 trace of a matrix is the sum of its diagonal elements.So on transposing the matrix the diagonal elements will ... is also equal to sum of eigen values.So trace of A = 7 So trace of transpose(A) should be 7. Is my reasoning right?
asked
Jan 3
in
Linear Algebra
by
vk_9_1_9
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123
points)

46
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matrix
0
votes
0
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39
Uppcl 2018
what could be the eigen values of a 2*2 Matrix if all its elements are intergers.
asked
Jan 2
in
Linear Algebra
by
Shashi Shekhar 1
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(
557
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53
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+26
votes
4
answers
40
GATE200623
$F$ is an $n\times n$ real matrix. $b$ is an $n\times 1$ real vector. Suppose there are two $n\times 1$ vectors, $u$ and $v$ such that, $u ≠ v$ and $Fu = b, Fv = b$. Which one of the following statements is false? Determinant of $F$ is zero. There are an infinite number of solutions to $Fx = b$ There is an $x≠0$ such that $Fx = 0$ $F$ must have two identical rows
answered
Jan 2
in
Linear Algebra
by
SameekshaGupta
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539
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1.9k
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gate2006
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