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Recent questions tagged matrix
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1
GATE 2017:EC
Consider the $5\times 5$ matrix: $\begin{bmatrix} 1 & 2 &3 & 4 &5 \\ 5 &1 &2 & 3 &4 \\ 4& 5 &1 &2 &3 \\ 3& 4 & 5 & 1 &2 \\ 2&3 & 4 & 5 & 1 \end{bmatrix}$ It is given $A$ has only one real eigen value. Then the real eigen value of $A$ is ________
asked
Jun 2
in
Linear Algebra
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srestha
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113k
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105
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discretemathematics
linearalgebra
matrix
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4
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2
GATE2017 EC
The rank of the matrix $\begin{bmatrix} 1 & 1 & 0 &0 & 0\\ 0 & 0 & 1 &1 &0 \\ 0 &1 &1 &0 &0 \\ 1 & 0 &0 & 0 &1 \\ 0&0 & 0 & 1 & 1 \end{bmatrix}$ is ________. Ans 5?
asked
Jun 1
in
Linear Algebra
by
srestha
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113k
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151
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discretemathematics
matrix
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1
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3
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)
asked
Jan 24
in
Linear Algebra
by
Nandkishor3939
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1.1k
points)

137
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engineeringmathematics
linearalgebra
matrices
rankofmatrix
matrix
0
votes
1
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4
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.
asked
Jan 19
in
Linear Algebra
by
Reshu $ingh
(
253
points)

124
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linearalgebra
matrix
eigenvalue
0
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0
answers
5
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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111
points)

70
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matrix
0
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0
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6
Wiki example  Rouché–Capelli_theorem
What is the rank of the augmented matrix and coefficient matrix here ? x + y + 2z = 3, x + y + z = 1, 2x + 2y + 2z = 2 The example says it’s Augmented Matrix Rank is 3 and Coefficent Matrix Rank is 2, Can someone share the solution using echelon Form? This is a question from wiki page example here
asked
Jan 1
in
Set Theory & Algebra
by
Salazar
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24
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matrix
rankofmatrix
discretemathematics
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7
Linearity of Matrix
$1)$What is linearly independent solution? Why it is depend on rank of matrix? (Linearly independent solution = no of rows of matrix rank of matrix) $I=NR$ $2)$ Why for unique solution of a matrix , determinant of matrix need to be nonzero? What should be determinant value for infinite solution?
asked
Nov 16, 2018
in
Linear Algebra
by
srestha
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113k
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53
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matrix
0
votes
0
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8
Derive formula of the Matrix
How formula $Ae=e$ is valid? Can someone give an example? Here that formula is used here but I gavenot got clearity how this formula can be correct?
asked
Nov 9, 2018
in
Linear Algebra
by
srestha
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113k
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46
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matrix
+1
vote
1
answer
9
Find Inverse
Inverse of this matrix $\begin{bmatrix} 2 &1 &1 \\ 3 &2 &1 \\ 2& 1 &2 \end{bmatrix}$ will be A)$\begin{bmatrix} 3 &4 &1 \\ 1 &2 &0 \\ 1 &1 &1 \end{bmatrix}$ B)$\begin{bmatrix} 3 &1 &1 \\ 4 &2 &1 \\ 1& 0 &1 \end{bmatrix}$
asked
Nov 3, 2018
in
Linear Algebra
by
srestha
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113k
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69
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engineeringmathematics
matrix
+1
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0
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10
LINEAR ALGEBRA
IF A=$\begin{bmatrix} 2& 0.1\\ 0 & 3 \end{bmatrix}$ AND A1=$\begin{bmatrix} \frac{1}{2}& a\\ 0 & b \end{bmatrix}$ then a+b ? a)$\frac{7}{20}$ b)$\frac{3}{20}$ c)$\frac{19}{60}$ d)$\frac{11}{20}$
asked
Oct 27, 2018
in
Linear Algebra
by
altamash
(
429
points)

63
views
matrix
+2
votes
1
answer
11
Linear algebra
For matrix $p=\begin{bmatrix} 3 &2 &2 \\ 0 &2 &1 \\ 0& 0 & 1 \end{bmatrix}$if one of the eigen values is equal to – 2, then which of the following is an eigen vector? (a) [ 3 −2 1 ] (b) [ −3 2 −1 ] (c) [ 1 −2 3 ] (d) [ 5 2 0 ]
asked
Oct 21, 2018
in
Linear Algebra
by
sahil_malik
Junior
(
561
points)

182
views
matrix
linearalgebra
+1
vote
2
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12
Virtual Gate Test Series: Linear Algebra  Rank Of The Matrix
asked
Oct 15, 2018
in
Linear Algebra
by
Prince Sindhiya
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5.4k
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62
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engineeringmathematics
linearalgebra
matrix
rankofmatrix
virtualgatetestseries
0
votes
0
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13
Invertible Matrix
Let $A$ be a nilpotent matrix. Show that $I + A$ is invertible.
asked
Aug 8, 2018
in
Linear Algebra
by
pankaj_vir
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10.4k
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89
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engineeringmathematics
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matrices
matrix
0
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2
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14
Invertible Matrix
Let A be a $5 × 5$ invertible matrix with row sums $1$. That is $\sum_{j=1}^{5} a_{ij} = 1$ for $1 \leq i\leq 5$. Then, what is the sum of all entries of $A^{1}$.
asked
Aug 8, 2018
in
Linear Algebra
by
pankaj_vir
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10.4k
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151
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engineeringmathematics
linearalgebra
matrices
matrix
easy
0
votes
1
answer
15
Rank of a matrix
Let A be a 4×3 real matrix with rank 2. Let B be transpose matrix of A. Which one of the following statement is TRUE? (a) Rank of BA is less than 2. (b) Rank of BA is equal to 2. (c) Rank of BA is greater than 2. (d) Rank of BA can be any number between 1 and 3.
asked
Jun 21, 2018
in
Mathematical Logic
by
bts
(
119
points)

185
views
rankofmatrix
engineeringmathematics
matrix
0
votes
0
answers
16
Gilbert Strang  Real Symmetric Matrices
Prove that : For all real symmetric matrices , No. of positive Pivots = No . of positive eigenvalues Can anyone please give the formal mathematical proof for the above statement ?
asked
Jun 2, 2018
in
Linear Algebra
by
ankitgupta.1729
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14k
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66
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linearalgebra
gilbertstrang
matrix
engineeringmathematics
0
votes
1
answer
17
Gilbert Strang 1.3.9
For which three numbers $k$ does elimination break down? Which is fixed by a row exchange? In each case, is the number of solutions $0$ or $1$ Infinity? $Kx + 3 y =6\\3x +ky = 6$
asked
May 31, 2018
in
Engineering Mathematics
by
Sandy Sharma
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1.2k
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93
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linearalgebra
gilbertstrang
matrix
0
votes
1
answer
18
self doubt
if $A^{3} = 0$ can we conclude that $A^{2} = A$ that will be valid for zero matrix
asked
Mar 4, 2018
in
Linear Algebra
by
Kaluti
Loyal
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5.4k
points)

71
views
matrix
+1
vote
1
answer
19
Ee gate 2008
Let $P$ be a $2$ x $2$ real orthogonal matrix and ${\vec{x}}$ is a real vector $[x_1,x_2]^T$ with length ${\vec{x}}$ = ${(x_1^2 + x_2^2)^{1/2}}$. Then which one of the following statements is correct? A. $P{\vec{x}}$ $\leq$ ${\vec{x}}$ where ... satisfies $P{\vec{x}}$ >${\vec{x}}$ D. No relationship can be established between${\vec{x}}$ and $P{\vec{x}}$
asked
Mar 4, 2018
in
Linear Algebra
by
Prince Sindhiya
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5.4k
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159
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gate2008ee
engineeringmathematics
matrix
vectorspace
0
votes
0
answers
20
Ee gate 2008
Let $P$ be a $2$ x $2$ real orthogonal matrix and ${\vec{x}}$ ia real vector $[x_1,x_2]^T$ with length ${\vec{x}}$ = ${(x_1^2 + x_2^2)^{1/2}}$. Then which one of the following statements is correct? A. $P{\vec{x}}$ $\leq$ ${\vec{x}}$ where at ... satisfies $P{\vec{x}}$ >${\vec{x}}$ D. No relationship can be established between${\vec{x}}$ and $P{\vec{x}}$
asked
Mar 3, 2018
in
Linear Algebra
by
Prince Sindhiya
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5.4k
points)

67
views
engineeringmathematics
matrix
+6
votes
1
answer
21
Eigen value
asked
Jan 13, 2018
in
Linear Algebra
by
Lakshman Patel RJIT
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44.6k
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169
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engineeringmathematics
linearalgebra
matrix
eigenvalue
+4
votes
1
answer
22
matrix adjoint
If $1,2,3$ are the eigen values of the matrix $A$ then ratio of determinant of $B$ to the trace of $B$ is_______where $B=[adj(A)AA^{1}A^{2}]$
asked
Jan 10, 2018
in
Linear Algebra
by
Lakshman Patel RJIT
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44.6k
points)

129
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engineeringmathematics
linearalgebra
matrix
0
votes
0
answers
23
ISRO GATE
The answer is given as (A) but according to me it should be (B). Can anyone explain please?
asked
Dec 5, 2017
in
Programming
by
Aakanchha
Junior
(
655
points)

76
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programminginc
matrix
+5
votes
1
answer
24
Matrix Eigen Value
A 3× 3 real matrix has an eigen value i, then its other two eigen values can be (A) 0, 1. (B) 1, i. (C) 2i, 2i. (D) 0, i.
asked
Nov 14, 2017
in
Mathematical Logic
by
Lakshman Patel RJIT
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44.6k
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150
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engineeringmathematics
linearalgebra
matrix
eigenvalue
+2
votes
0
answers
25
rank of matrix
The rank of the matrix of coefficients of a homogeneous system of m linear equations in n unknowns is never less than the rank of the augmented matrix. (A) Always true (B) Sometimes true (C) False (D) None of the above
asked
Nov 11, 2017
in
Linear Algebra
by
Parshu gate
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3.1k
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145
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rankofmatrix
matrix
linearalgebra
engineeringmathematics
+5
votes
1
answer
26
Gilbert Strang
How many n*n (0,1) matrix are invertable ? PS: original question in book is for 2*2
asked
Oct 23, 2017
in
Linear Algebra
by
Tesla!
Boss
(
18k
points)

130
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matrix
gilbertstrang
linearalgebra
+3
votes
1
answer
27
Find the last row of the Matrix
For the first one I have got 28 and 11 as the answer but for the matrix C I am not able to get the value of element c32. c31 = c33 = 6.
asked
Jul 24, 2017
in
Linear Algebra
by
Shubhanshu
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18k
points)

162
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engineeringmathematics
linearalgebra
matrix
eigenvalue
+6
votes
3
answers
28
Gate ECE 2017 Eigen Value
For the given matrix A, one of the Eigenvalue is real $A=\begin{bmatrix} 1 &2 &3 &4 &5 \\ 5 &1 &2 &3 &4 \\ 4&5 &1 &2 &3 \\ 3&4 &5 &1 &2 \\ 2 &3 &4 &5 &1 \end{bmatrix}$ The real Eigen value is:
asked
Feb 8, 2017
in
Linear Algebra
by
yg92
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3.1k
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1.4k
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matrix
eigenvalue
+3
votes
1
answer
29
MATRIX
Let A be a $3 \times 3$ matrix with integer entries such that $A =1$. What is the maximum possible number of entries of A that are even?
asked
Jan 19, 2017
in
Set Theory & Algebra
by
Supremo
(
377
points)

261
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matrix
matrices
linearalgebra
discretemathematics
0
votes
0
answers
30
Matrix
1. If the row reduced form of a matrix has more than two nonzero entries in a row, then the corresponding system of equations has infinitely many solutions. 2. If the row reduced form of a matrix has more than two nonzero entries in a row, then the ... many solutions or no solution. The given statements are respectively A. True, True B. True, False C. False, True D. False, False
asked
Jan 18, 2017
in
Linear Algebra
by
Samujjal Das
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9.2k
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64
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matrix
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