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Recent questions tagged linear-algebra

0 votes
1 answer
511
linear algebra
A is m×n full rank matrix with m>n and 1 is an identity matrix. Let matrix A’ = (ATA)-1 AT. Then which one of the following statement is FALSE? (a) AA’A = A (b) (AA’)2 (c) AA’A = 1 (d) AA’A = A’
A is m×n full rank matrix with m>n and 1 is an identity matrix. Let matrix A’ = (ATA)-1 AT. Then which one of the following statement is FALSE?(a) AA’A = A (b) (AA�...
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0 votes
2 answers
513
linear algebra
If w cube root of – 1, then find value of deteminant [1 −w w2] [ −w w2 1 ] [ w2 1 w ]
If w cube root of – 1, then find value of deteminant [1 −w w2] ...
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1 votes
1 answer
514
eigen vector
An arbitrary vector X is an eigen vector of the vector of the matrix A=[1 0 0 a 0 0 0 0 b], if (a, b)= (a) (0, 0) (b) (1, 1) (c) (0, 1) (d) (1, 2)
An arbitrary vector X is an eigen vector of the vector of the matrix A=[1 0 0 a 0 0 0 0 b], if (a, b)=(a) (0, 0) (b) (1, 1)(c) (0, 1) (d) (1, 2)
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2 votes
3 answers
516
Mathematics GATE 2018 EE: 44
Let $A$ = $\begin{bmatrix} 1 & 0 & -1 \\-1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B$ = $A^{3} - A^{2} -4A +5I$ where $I$ is the $3\times 3$ identity matrix. The determinant of $B$ is ________ (up to $1$ decimal place).
Let $A$ = $\begin{bmatrix} 1 & 0 & -1 \\-1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B$ = $A^{3} - A^{2} -4A +5I$ where$I$ is the $3\times 3$ identity matrix. The de...
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24 votes
6 answers
518
GATE CSE 2018 | Question: 17
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The largest eigenvalue of $A$ is ____
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The larg...
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0 votes
0 answers
519
Eigen Vectors
I'm getting 2
I'm getting 2
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6 votes
1 answer
520
Made easy books GATE - 2015( IN ) 1 mark
Let $A$ be a $n\times n$ matrix with rank $ r ( 0 < r < n ) .$Then $AX = 0$ has $p$ independent solutions,where $p$ is $A)$ $r$ $B)$ $n$ $C)$ $n - r $ $D)$ $n + r$
Let $A$ be a $n\times n$ matrix with rank $ r ( 0 < r < n ) .$Then $AX = 0$ has $p$ independent solutions,where $p$ is$A)$ $r$ $B)$ $n$ $C)$ $n - r...
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7 votes
1 answer
521
LU decomposition
In the LU decomposition of the matrix,$\begin{bmatrix} 1 &2 \\ 3 &8 \end{bmatrix}$ if the diagonal elements of $U$ are both $1$, then the trace of $L$ is$?$
In the LU decomposition of the matrix,$\begin{bmatrix} 1 &2 \\ 3 &8 \end{bmatrix}$ if the diagonal elements of $U$ are both $1$, then the trace of $L$ is$?$
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4 votes
1 answer
522
largest eigen value
Assume determinant of a $3\times3$ matrix is a prime number and trace is $15.$Largest eigen value is _______(Assume only positve eigen values)
Assume determinant of a $3\times3$ matrix is a prime number and trace is $15.$Largest eigen value is _______(Assume only positve eigen values)
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1 votes
0 answers
525
Linear Algebra
If $I$ is the unit matrix of order $n$ , where $k!=0$ is a constant then $adj \ kI$ is
If $I$ is the unit matrix of order $n$ , where $k!=0$ is a constant then $adj \ kI$ is
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4 votes
1 answer
526
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 $B=[adj(A)-A-A^{-1}-A^{2}]$
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 $B=[adj(A)-A-A^{-1}-A^{2}]$
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3 votes
1 answer
527
matrix
Given that the matrix $A=\begin{bmatrix} 1 &2 &2 \\ 2 &1 &-2 \\ a& 2 &b \end{bmatrix}$ and $AAA^{T}=3I$ where $I$ is a $3\times3$ identity matrix$.$ Find $(a,b)$ can be$?$
Given that the matrix $A=\begin{bmatrix} 1 &2 &2 \\ 2 &1 &-2 \\ a& 2 &b \end{bmatrix}$ and $AAA^{T}=3I$ where $I$ is a $3\times3$ identity matrix$.$Find $(a,b)$ can be$?...
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4 votes
0 answers
529
Matrix
If $A$ and $B$ are symmetric matrices of the same order, then $AB-BA$ is NULL matrix Symmetric matrix Skew symmetric matrix Orthogonal matrix
If $A$ and $B$ are symmetric matrices of the same order, then $AB-BA$ isNULL matrixSymmetric matrixSkew symmetric matrixOrthogonal matrix
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2 votes
0 answers
530
made easy subject wise
A real n × n matrix A = {aij} is defined as follows: aij= i, if i = j, otherwise 0 The determinant of all n eigen values of A is
A real n × n matrix A = {aij} is defined as follows: aij= i, if i = j, otherwise 0The determinant of all n eigen values of A is
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2 votes
1 answer
531
MadeEasy Test Series: Linear Algebra - Matrices
If $A=\begin{bmatrix} cos \alpha & sin \alpha \\ -sin \alpha & cos \alpha \end{bmatrix}$ be such that $A +A ^{'}=I$ then the value of $\alpha$ is
If $A=\begin{bmatrix} cos \alpha & sin \alpha \\ -sin \alpha & cos \alpha \end{bmatrix}$be such that $A +A ^{'}=I$ then the value of $\alpha$ is
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2 votes
1 answer
533
Linear Algebra: Matrix operations
Consider two statements:- 1) Eigenvalue of M = Eigenvalue of M' {M' is the matrix gets after row operation} 2) Eigenvalue of |M- $\lambda$I| = Eigenvalue of |M- $\lambda$I|' {|M- $\lambda$I|' is the matrix gets after row operation}
Consider two statements:-1) Eigenvalue of M = Eigenvalue of M' {M' is the matrix gets after row operation}2) Eigenvalue of |M- $\lambda$I| = Eigenvalue of |M- $\lambda$I|...
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3 votes
1 answer
534
IN Gate 2007 - Matrix
Let A be an nxn real matrix such that A^2=I and y be an n-dimensional vector. Then the linear system of equations AX=Y has A) No solution B) Unique Solution C) More than one but finitely many independent solutions D) infinitely many independent solutions
Let A be an nxn real matrix such that A^2=I and y be an n-dimensional vector. Then the linear system of equations AX=Y hasA) No solutionB) Unique SolutionC) More than one...
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1 votes
0 answers
536
Domain of Mod-Trigo function ALLEN2017
For existence of f(x) = , x lies in (take n I) (1) [0, 2nπ] (2) (3) (4) None of these how to solve such question? Pl give detailed explanation. Always find difficult to solve Range and domain of such complex question.
For existence of f(x) = , x lies in (take n I)(1)[0, 2nπ](2)(3)(4)None of thesehow to solve such question? Pl give detailed explanation.Always find difficult to solve R...
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1 votes
2 answers
539
LU decomposition
Given the system of linear equations: $4y\ +\ 3z\ =\ 8\\ 2x\ -\ z\ =\ 2\\ 3x\ +\ 2y\ =\ 5$ Find L & U.
Given the system of linear equations:$4y\ +\ 3z\ =\ 8\\ 2x\ -\ z\ =\ 2\\ 3x\ +\ 2y\ =\ 5$Find L & U.
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