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Recent questions tagged linear-algebra

7 votes
1 answer
541
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
542
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
545
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
546
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
547
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
549
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
550
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
551
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
553
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
554
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
556
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
559
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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0 votes
0 answers
562
EE-GATE_2014_S1_2 Marks
A system matrix is given as follows. A = $\begin{pmatrix} 0 & 1 &-1 \\ -6 &-11 &6 \\ -6 & -11 & 5 \end{pmatrix}$ The absolute value of the ratio of the maximum eigen value to the minimum eigen value is ?
A system matrix is given as follows.A = $\begin{pmatrix} 0 & 1 &-1 \\ -6 &-11 &6 \\ -6 & -11 & 5 \end{pmatrix}$The absolute value of the ratio of the maximum eigen value ...
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1 votes
1 answer
563
ME: GATE-2005
A is a 3 x 4 real matrix and A x = b is an inconsistent system of equations. The highest possible rank of A is:____________
A is a 3 x 4 real matrix and A x = b is an inconsistent system of equations. Thehighest possible rank of A is:____________
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0 votes
0 answers
564
Matrices
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0 votes
0 answers
566
ME GATE 2016
The number of linearly independent eigenvectors of matrix A= $\begin{pmatrix} 2 &1 & 0\\ 0& 2 &0 \\ 0& 0 & 3 \end{pmatrix}$
The number of linearly independent eigenvectors of matrix A= $\begin{pmatrix} 2 &1 & 0\\ 0& 2 &0 \\ 0& 0 & 3 \end{pmatrix}$
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1 votes
1 answer
567
No.of no negative integer solutions
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0 votes
1 answer
569
Engineering Maths: Increasing function
If $f(x)$ is an increasing function ,then $(f(x))^2$ >$f(x)$ ? True/false
If $f(x)$ is an increasing function ,then $(f(x))^2$ >$f(x)$ ? True/false
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3 votes
1 answer
570
System equation of matrix
If 3x+2y+z= 0, x+4y+z=0, 2x+y+4z=0, be a system of equations then (A) the system is inconsistent (B) it has the only trivial solution (C) it can be reduced to a single equation thus solution does not exist (D) a determinant of the coefficient matrix is zero.
If 3x+2y+z= 0, x+4y+z=0, 2x+y+4z=0, be a system of equations then(A) the system is inconsistent(B) it has the only trivial solution(C) it can be reduced to a single equat...
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