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Webpage for Linear Algebra
Recent questions tagged linear-algebra
1
votes
1
answer
661
Find the Eigen Vector
Find the Eigenvector of $\begin{bmatrix} 1 & cos\theta\\ cos \theta & 1 \end{bmatrix}$
Find the Eigenvector of $\begin{bmatrix} 1 & cos\theta\\ cos \theta & 1 \end{bmatrix}$
Anuanu
1.6k
views
Anuanu
asked
Jun 2, 2016
Linear Algebra
linear-algebra
matrix
+
–
9
votes
1
answer
662
ISRO2008-31
If the two matrices $\begin{bmatrix} 1 &0 &x \\ 0 & x& 1\\ 0 & 1 & x \end{bmatrix}$ and $\begin{bmatrix} x &1 &0 \\ x & 0& 1\\ 0 & x & 1 \end{bmatrix}$ have the same determinant, then the value of $x$ is $\frac{1}{2}$ $\sqrt2$ $\pm \frac{1}{2}$ $\pm \frac{1}{\sqrt2}$
If the two matrices $\begin{bmatrix} 1 &0 &x \\ 0 & x& 1\\ 0 & 1 & x \end{bmatrix}$ and $\begin{bmatrix} x &1 &0 \\ x & 0& 1\\ 0 & x & 1 \end{bmatrix}$ have the same dete...
jaiganeshcse94
2.3k
views
jaiganeshcse94
asked
May 31, 2016
Linear Algebra
isro2008
linear-algebra
matrix
determinant
+
–
0
votes
2
answers
663
GATE 2012 ME HOW TO NORMAIZE EIGEN VECTORS
pC
573
views
pC
asked
May 3, 2016
Linear Algebra
linear-algebra
+
–
0
votes
0
answers
664
Eigen values and characteristic equation
I have learned a shortcut for finding eigen values and characteristic equation. It is as follows. $\lambda ^{_{3}}- \alpha \lambda ^{2}+ \beta \lambda - \gamma =0$ where $ \alpha =$ trace of 3*3 matrix $ \beta =$ sum of ... problem I'm stuck, Could any one help me find why I'm stuck . I was getting answer using this trick for almost all problems
I have learned a shortcut for finding eigen values and characteristic equation. It is as follows.$\lambda ^{_{3}}- \alpha \lambda ^{2}+ \beta \lambda - \gamma =0$where $ ...
pC
3.1k
views
pC
asked
May 1, 2016
Linear Algebra
eigen-value
linear-algebra
+
–
10
votes
1
answer
665
ISRO-2013-33
What is the matrix transformation which takes the independent vectors $\begin{pmatrix} 1& \\ 2& \end{pmatrix}$ and $\begin{pmatrix} 2& \\ 5& \end{pmatrix}$ and transforms them to $\begin{pmatrix} 1& \\ 1& \end{pmatrix}$ ... $\begin{pmatrix} -1&0 \\ 1& 1 \end{pmatrix}$ $\begin{pmatrix} -1&1 \\ 1& 0 \end{pmatrix}$
What is the matrix transformation which takes the independent vectors $\begin{pmatrix}1& \\2& \end{pmatrix}$ and $\begin{pmatrix}2& \\5& \end{pmatrix}$ and transforms the...
makhdoom ghaya
3.8k
views
makhdoom ghaya
asked
Apr 27, 2016
Linear Algebra
isro2013
linear-algebra
eigen-value
+
–
49
votes
10
answers
666
GATE CSE 2016 Set 1 | Question: 05
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______
Sandeep Singh
14.5k
views
Sandeep Singh
asked
Feb 12, 2016
Linear Algebra
gatecse-2016-set1
linear-algebra
eigen-value
numerical-answers
normal
+
–
37
votes
2
answers
667
GATE CSE 2016 Set 2 | Question: 06
Suppose that the eigenvalues of matrix $A$ are $1, 2, 4$. The determinant of $\left(A^{-1}\right)^{T}$ is _________.
Suppose that the eigenvalues of matrix $A$ are $1, 2, 4$. The determinant of $\left(A^{-1}\right)^{T}$ is _________.
Akash Kanase
11.5k
views
Akash Kanase
asked
Feb 12, 2016
Linear Algebra
gatecse-2016-set2
linear-algebra
eigen-value
normal
numerical-answers
+
–
54
votes
7
answers
668
GATE CSE 2016 Set 2 | Question: 04
Consider the systems, each consisting of $m$ linear equations in $n$ variables. If $m < n$, then all such systems have a solution. If $m > n$, then none of these systems has a solution. If $m = n$, then there exists a system which has a solution. ... $\text{II}$ and $\text{III}$ are true. Only $\text{III}$ is true. None of them is true.
Consider the systems, each consisting of $m$ linear equations in $n$ variables.If $m < n$, then all such systems have a solution.If $m n$, then none of these systems has...
Akash Kanase
15.7k
views
Akash Kanase
asked
Feb 12, 2016
Linear Algebra
gatecse-2016-set2
linear-algebra
system-of-equations
normal
+
–
2
votes
5
answers
669
linearalgebra
if $A = \begin{bmatrix} 2 &3 &4 \\ 3 & -1 &2 \\ -1& 4 & 5 \end{bmatrix}$ then rank of the matrix $(A-A^T)$ is _____ (A) $1$ (B) $2$ (C) $3$ (D) $0$
if $A = \begin{bmatrix} 2 &3 &4 \\ 3 & -1 &2 \\ -1& 4 & 5 \end{bmatrix}$ then rank of the matrix $(A-A^T)$ is _____(A) $1$ (B) $2$ (C...
Registered user 7
834
views
Registered user 7
asked
Feb 3, 2016
Linear Algebra
matrix
linear-algebra
+
–
0
votes
1
answer
670
A set of r vectors with r < n elements are always Linearly Independent How?
Let r = No. of Vectors and n = No. of elements in each vector A set of r vectors with r < n elements are always Linearly Independent, provided the vectors should not be in the same direction. Can anyone please explain How?
Let r = No. of Vectors and n = No. of elements in each vectorA set of r vectors with r < n elements are always Linearly Independent, provided the vectors should not be in...
Prashant Gupta
449
views
Prashant Gupta
asked
Feb 3, 2016
Linear Algebra
linear-algebra
+
–
0
votes
1
answer
671
Orthogonal set of vectors in R
What is R in this question? How to solve this? Q).Let $A$ be a real $n*n$ matrix ,then which of the following statements are true? I). $A$ is orthogonal iff the row vectors form an orthgonal set of vectors in $R^4$. II). $A$ is orthogonal iff the columns ... of vectors in $R^4$. (A) Only I (B) Only II (C) Both I and II (D) None of these The correct answer is C.
What is R in this question? How to solve this?Q).Let $A$ be a real $n*n$ matrix ,then which of the following statements are true?I). $A$ is orthogonal iff the row vectors...
Purple
856
views
Purple
asked
Jan 31, 2016
Linear Algebra
linear-algebra
eigen-value
engineering-mathematics
+
–
0
votes
0
answers
672
Eigen vectors of linear equation defined by cross product
How to solve this question?
How to solve this question?
Purple
527
views
Purple
asked
Jan 31, 2016
Linear Algebra
linear-algebra
eigen-value
engineering-mathematics
+
–
0
votes
2
answers
673
Maths: LA Non Homogeneous Equation
Given the following set of equations: X - y - z = 0 x + y + z = 46 x - 2y +z = 16 -x - y + 2z = -7 which of the following is true ? a) no solution b) infinite many solution c) exactly one solution d) exactly one solution and atleast one of the x,y,z is negative
Given the following set of equations:X - y - z = 0x + y + z = 46x - 2y +z = 16-x - y + 2z = -7which of the following is true ?a) no solutionb) infinite many solutionc) ex...
Prasanna
524
views
Prasanna
asked
Jan 31, 2016
Linear Algebra
linear-algebra
+
–
0
votes
1
answer
674
Virtual Gate Test Series: Linear Algebra - Matrix(Number Of Solutions)
$1)$ If the row reduced the form of a matrix has more than two non-zero entries in any row, then the corresponding system of equations has Infinitely many solutions. $2)$ If the row reduced the form of a matrix has more ... 2 non zero, then it's good, because then we will have more number of equations? How is the answer C?
$1)$ If the row reduced the form of a matrix has more than two non-zero entries in any row, then the corresponding system of equations has Infinitely many solutions.$2)$ ...
Purple
1.4k
views
Purple
asked
Jan 30, 2016
Linear Algebra
engineering-mathematics
linear-algebra
matrix
number-of-solutions
virtual-gate-test-series
+
–
1
votes
1
answer
675
Ace Test Series: Linear Algebra - Eigen Value
Answer should be A. But they gave D. Their Explanation: Corresponding to each distinct eigen value, we have atleast one independent eigen vector.
Answer should be A. But they gave D. Their Explanation: Corresponding to each distinct eigen value, we have atleast one independent eigen vector.
Tushar Shinde
1.6k
views
Tushar Shinde
asked
Jan 30, 2016
Linear Algebra
ace-test-series
engineering-mathematics
linear-algebra
eigen-value
+
–
5
votes
1
answer
676
eigen values
The linear operation $L(x)$ is defined by the cross product $L(x)= b \times x$, where $b=\left[0 1 0\right]^{T}$ and $x=\left[x_{1} x_{2} x_{3}\right]^{T}$ are three dimensional vectors. The $3 \times 3$ matrix $M$ ... $M$ are $0, +1, -1$ $1, -1, 1$ $i, -i, 1$ $i, -i, 0$
The linear operation $L(x)$ is defined by the cross product $L(x)= b \times x$, where $b=\left[0 1 0\right]^{T}$ and $x=\left[x_{1} x_{2} x_{3}\right]^{T}$ are three dime...
sourav.
2.0k
views
sourav.
asked
Jan 25, 2016
Linear Algebra
linear-algebra
eigen-value
engineering-mathematics
+
–
0
votes
1
answer
677
Math Linear Algebra
If A and B are real symmetric matrices of size n*n. Then, which one of the following is true? a) AA^t = I b) A = A^-1 c) AB =BA d) (AB)^t = BA
If A and B are real symmetric matrices of size n*n. Then, which one of the following is true?a) AA^t = Ib) A = A^-1c) AB =BAd) (AB)^t = BA
Cruise Device
902
views
Cruise Device
asked
Jan 21, 2016
Linear Algebra
engineering-mathematics
linear-algebra
+
–
0
votes
0
answers
678
Math Linear Algebra
If a,b and c are constants, which of the following is a linear inequality? a) ax + bcy = 0 b) ax^2 + cy = 21 c) abx + a^2y >= 15 d) xy + ax >= 20
If a,b and c are constants, which of the following is a linear inequality?a) ax + bcy = 0b) ax^2 + cy = 21c) abx + a^2y >= 15d) xy + ax >= 20
Cruise Device
372
views
Cruise Device
asked
Jan 21, 2016
Linear Algebra
engineering-mathematics
linear-algebra
+
–
0
votes
0
answers
679
groups
Pranav Gupta 1
202
views
Pranav Gupta 1
asked
Jan 20, 2016
Linear Algebra
linear-algebra
matrix
+
–
0
votes
2
answers
680
Determinant of matrix
What is the determinant of matrix 2A. determinant of matrix A is 3. and IT is 4 by 4 matrix?
What is the determinant of matrix 2A. determinant of matrix A is 3. and IT is 4 by 4 matrix?
Pradip Nichite
1.4k
views
Pradip Nichite
asked
Jan 18, 2016
Linear Algebra
linear-algebra
matrix
+
–
0
votes
0
answers
681
linear algebra
let A be a diagonalizable matrix of order n*n .then which of the following is true? a)A has atleast one Linearly Independent Eigen vector b)A has atleast n Linearly Dependent Eigen vector c)A has exactly one Linearly Independent Eigen vector d)A has exactly n Linearly Dependent Eigen vector
let A be a diagonalizable matrix of order n*n .then which of the following is true?a)A has atleast one Linearly Independent Eigen vectorb)A has atleast n Linearly Depende...
sourav.
332
views
sourav.
asked
Jan 14, 2016
Linear Algebra
linear-algebra
+
–
7
votes
2
answers
682
ME GATE 2012 What is Normalised Eigen Vector ?
For the Matrix $\begin{bmatrix} 5 & 3\\ 1& 3 \end{bmatrix}$ One of the Normalised Eigen Vector is given as__________ Answer $\begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{-1}{\sqrt{2}} \end{bmatrix}$ What is Normalised Eigen Vector ? How to Find the Solution ?
For the Matrix $\begin{bmatrix} 5 & 3\\ 1& 3 \end{bmatrix}$One of the Normalised Eigen Vector is given as__________Answer $\begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{-1...
pC
5.8k
views
pC
asked
Jan 7, 2016
Linear Algebra
linear-algebra
gate2012me
eigen-value
+
–
0
votes
0
answers
683
GATE 2014 _ 28 [IN]
A scalar valued function is defined as $f(x) = x^T Ax + b^Tx + c$ where A = symmetric +ve definite matrix with diamension n*n x = are vectors of dimension n* 1 The min value of f(x) will occur when x equals (ATA )-1B - (ATA )-1B -(A-1B) / 2 (A-1B) / 2
A scalar valued function is defined as$$f(x) = x^T Ax + b^Tx + c$$where A = symmetric +ve definite matrix with diamension n*n x = are vectors of dimension n* ...
pC
784
views
pC
asked
Jan 7, 2016
Linear Algebra
linear-algebra
+
–
1
votes
1
answer
684
Matrix multiplication 1
I want to ask about the equation i hv marked a question mark. (p-1qp)n=p-1qnp how?? Why is there no power on matrix p ?
I want to ask about the equation i hv marked a question mark.(p-1qp)n=p-1qnp how??Why is there no power on matrix p ?
khushtak
779
views
khushtak
asked
Jan 4, 2016
Linear Algebra
matrix
linear-algebra
+
–
0
votes
1
answer
685
Linear Algebra Doubt
while solving linear equations, there comes a case where rank < number of varibles, then we say there are n-r linearly independent solution. What exactly does it mean ?
while solving linear equations, there comes a case where rank < number of varibles,then we say there are n-r linearly independent solution.What exactly does it mean ?
Sandeep Singh
511
views
Sandeep Singh
asked
Jan 4, 2016
Linear Algebra
engineering-mathematics
linear-algebra
+
–
1
votes
2
answers
686
matrix
resuscitate
1.3k
views
resuscitate
asked
Jan 3, 2016
Linear Algebra
matrix
linear-algebra
+
–
0
votes
1
answer
687
matrix
how to solve??
how to solve??
resuscitate
569
views
resuscitate
asked
Jan 3, 2016
Linear Algebra
matrix
linear-algebra
+
–
3
votes
2
answers
688
Gate_2007 ME
The number of linearly independent Eigen vectors of is a) 0 b) 1 C) 2 d) infinite
The number of linearly independent Eigen vectors of is a) 0b) 1 C) 2d) infinite
Himanshu1
11.0k
views
Himanshu1
asked
Jan 2, 2016
Linear Algebra
engineering-mathematics
linear-algebra
eigen-value
+
–
3
votes
1
answer
689
GATE_2014 ME
Consider a 3 x 3 real symmetric matrix S such that two of its eigen values are a ≠ 0 , b ≠ 0 with respective Eigen vectors [ x1 x2 x3 ] , [ y1 y2 y3 ] . If a ≠ b then x1y1 + x2y2 + x3y3 is a) a b) b c) ab d) 0
Consider a 3 x 3 real symmetric matrix S such that two of its eigen values are a ≠ 0 , b ≠ 0 with respective Eigen vectors [ x1 x2 x3 ] , [ y1 y2 y3 ] . If a &ne...
Himanshu1
2.4k
views
Himanshu1
asked
Jan 2, 2016
Linear Algebra
engineering-mathematics
linear-algebra
eigen-value
+
–
3
votes
1
answer
690
Eigen Values of special matrices
A) what are the eigen values of Orthogonal matrix ? Describe general properties. B) what are the Eigen value of skew-symmetric matrix ? Describe general properties. C) Are there any speciality in Eigen values of Symmetric, Hermitian, Skew- Hermitian, Unitary . If there , describe them also.
A) what are the eigen values of Orthogonal matrix ? Describe general properties.B) what are the Eigen value of skew-symmetric matrix ? Describe general properties.C) Are ...
Himanshu1
1.6k
views
Himanshu1
asked
Jan 1, 2016
Linear Algebra
engineering-mathematics
eigen-value
linear-algebra
+
–
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