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Recent questions tagged linear-algebra
0
votes
2
answers
721
Which of the following statement is incorrect ?
worst_engineer
asked
in
Linear Algebra
Sep 19, 2015
by
worst_engineer
1.5k
views
linear-algebra
0
votes
1
answer
722
How to calculate LU decomposition of a 2*2 matrix ?
I need to calculate determinant of a 2*2 matrix such as $\begin{bmatrix} 2 &2 \\ 4& 9 \end{bmatrix}$ I proceeded by making it a upper triangular matrix and then using the negetives of the multipliers to get the lower triangular matrix. ... But the product of L and U is not coming out to be equal to the orig matrix. What am I doing wrong ?
learncp
asked
in
Linear Algebra
Sep 11, 2015
by
learncp
4.2k
views
linear-algebra
matrix
0
votes
1
answer
723
why row rank of a matrix is equal to column rank of the matrix ?
suraj
asked
in
Linear Algebra
Aug 26, 2015
by
suraj
1.0k
views
matrix
linear-algebra
1
vote
2
answers
724
For what value of a, if any, will the following system of equations in x, y and z have a solution?
For what value of a, if any, will the following system of equations in x, y and z have a solution? 2x + 3y = 4, x + y + z = 4, x + 2y – z = a (a) Any real number (b) 0 (c) 1 (d) There is no such value
learncp
asked
in
Linear Algebra
Aug 25, 2015
by
learncp
3.3k
views
linear-algebra
0
votes
2
answers
725
A is a 4-square matrix and A 5 = 0. Then
A is a 4-square matrix and A_5 (a raised to the power of 5) = 0. Then A_4 = a) I b) -I c) 0 d) A
learncp
asked
in
Linear Algebra
Aug 25, 2015
by
learncp
4.5k
views
matrix
linear-algebra
1
vote
1
answer
726
A be a n-square matrix with integer entries and B = A + 12 I. Then
A be a n-square matrix with integer entries and B = A + 12 I. Then (a) B is idempotent (b) B inverse exist (c) B is nilpotent (d) B inverse is idempotent
learncp
asked
in
Linear Algebra
Aug 25, 2015
by
learncp
2.0k
views
linear-algebra
matrix
1
vote
2
answers
727
A is an upper triangular with all diagonal entries zero, then I+A is
A is an upper triangular with all diagonal entries zero, then I+A is (a) invertible (b) idempotent (c) singular (d) nilpotent
learncp
asked
in
Linear Algebra
Aug 25, 2015
by
learncp
11.2k
views
linear-algebra
matrix
1
vote
2
answers
728
Let Mn×n be the set of all n-square symmetric matrices and the characteristics polynomial of each A∈Mn×n is...
learncp
asked
in
Linear Algebra
Aug 25, 2015
by
learncp
3.1k
views
linear-algebra
matrix
33
votes
5
answers
729
GATE CSE 2015 Set 3 | Question: 33
If the following system has non-trivial solution, $px + qy + rz = 0$ $qx + ry + pz = 0$ $rx + py + qz = 0$, then which one of the following options is TRUE? $p - q + r = 0 \text{ or } p = q = -r$ $p + q - r = 0 \text{ or } p = -q = r$ $p + q + r = 0 \text{ or } p = q = r$ $p - q + r = 0 \text{ or } p = -q = -r$
go_editor
asked
in
Linear Algebra
Feb 15, 2015
by
go_editor
10.8k
views
gatecse-2015-set3
linear-algebra
system-of-equations
normal
31
votes
9
answers
730
GATE CSE 2015 Set 3 | Question: 15
In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is $1.$ The eigenvectors corresponding to the eigenvalue $1$ ... $\left\{a\left(- \sqrt{2},0,1\right) \mid a \neq 0, a \in \mathbb{R}\right\}$
go_editor
asked
in
Linear Algebra
Feb 14, 2015
by
go_editor
17.6k
views
gatecse-2015-set3
linear-algebra
eigen-value
normal
27
votes
5
answers
731
GATE CSE 2015 Set 1 | Question: 36
Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$. The eigenvalues of this matrix are $-1$ and $7.$ What are the values of $a$ and $b$? $\qquad A = \begin{pmatrix}1 & 4\\ b&a \end{pmatrix}$ $a = 6, b = 4$ $a = 4, b = 6$ $a = 3, b = 5$ $a = 5, b = 3 $
makhdoom ghaya
asked
in
Linear Algebra
Feb 13, 2015
by
makhdoom ghaya
6.7k
views
gatecse-2015-set1
linear-algebra
eigen-value
easy
32
votes
5
answers
732
GATE CSE 2015 Set 1 | Question: 18
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_________________.
makhdoom ghaya
asked
in
Linear Algebra
Feb 13, 2015
by
makhdoom ghaya
11.6k
views
gatecse-2015-set1
linear-algebra
matrix
numerical-answers
35
votes
4
answers
733
GATE CSE 2015 Set 2 | Question: 27
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 _____.
go_editor
asked
in
Linear Algebra
Feb 12, 2015
by
go_editor
7.3k
views
gatecse-2015-set2
linear-algebra
matrix
easy
numerical-answers
23
votes
3
answers
734
GATE CSE 2015 Set 2 | Question: 5
The larger of the two eigenvalues of the matrix $\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ is _______.
go_editor
asked
in
Linear Algebra
Feb 12, 2015
by
go_editor
7.5k
views
gatecse-2015-set2
linear-algebra
eigen-value
easy
numerical-answers
1
vote
1
answer
735
Factor of determinant with identical row
How the following fact applies to determinants (I came across it while solving problems): Consider A is a n× n matrix, the elements of which are real (or complex) polynomials in x. If r rows of the determinant become identical when x ... is collapsing of rows of matrix (into one row) with order of its factors. Am I missing some stupid fact here?
Mahesha999
asked
in
Linear Algebra
Dec 3, 2014
by
Mahesha999
1.9k
views
matrix
linear-algebra
polynomials
29
votes
8
answers
736
GATE IT 2005 | Question: 3
The determinant of the matrix given below is $\begin{bmatrix} 0 &1 &0 &2 \\ -1& 1& 1& 3\\ 0&0 &0 & 1\\ 1& -2& 0& 1 \end{bmatrix}$ $-1$ $0$ $1$ $2$
Ishrat Jahan
asked
in
Linear Algebra
Nov 3, 2014
by
Ishrat Jahan
20.3k
views
gateit-2005
linear-algebra
normal
determinant
21
votes
4
answers
737
GATE IT 2004 | Question: 36
If matrix $X = \begin{bmatrix} a & 1 \\ -a^2+a-1 & 1-a \end{bmatrix}$ and $X^2 - X + I = O$ ($I$ is the identity matrix and $O$ is the zero matrix), then the inverse of $X$ is $\begin{bmatrix} 1-a &-1 \\ a^2& a \end{bmatrix}$ ... $\begin{bmatrix} -a &1 \\ -a^2+a-1& 1-a \end{bmatrix}$ $\begin{bmatrix} a^2-a+1 &a \\ 1& 1-a \end{bmatrix}$
Ishrat Jahan
asked
in
Linear Algebra
Nov 2, 2014
by
Ishrat Jahan
4.2k
views
gateit-2004
linear-algebra
matrix
normal
45
votes
3
answers
738
GATE IT 2004 | Question: 32
Let $A$ be an $n \times n$ ...
Ishrat Jahan
asked
in
Linear Algebra
Nov 2, 2014
by
Ishrat Jahan
7.9k
views
gateit-2004
linear-algebra
matrix
normal
17
votes
5
answers
739
GATE IT 2004 | Question: 6
What values of x, y and z satisfy the following system of linear equations? $\begin{bmatrix} 1 &2 &3 \\ 1& 3 &4 \\ 2& 2 &3 \end{bmatrix} \begin{bmatrix} x\\y \\ z \end{bmatrix} = \begin{bmatrix} 6\\8 \\ 12 \end{bmatrix}$ $x = 6$, $y = 3$, $z = 2$ $x = 12$, $y = 3$, $z = - 4$ $x = 6$, $y = 6$, $z = - 4$ $x = 12$, $y = - 3$, $z = 0$
Ishrat Jahan
asked
in
Linear Algebra
Nov 1, 2014
by
Ishrat Jahan
6.4k
views
gateit-2004
linear-algebra
system-of-equations
easy
1
vote
1
answer
740
GATE IT 2006 | Question: 77
$x + y/2 = 9$ $3x + y = 10$ What can be said about the Gauss-Siedel iterative method for solving the above set of linear equations? it will converge It will diverse It will neither converge nor diverse It is not applicable
Ishrat Jahan
asked
in
Linear Algebra
Nov 1, 2014
by
Ishrat Jahan
1.7k
views
gateit-2006
linear-algebra
normal
numerical-methods
non-gate
1
vote
1
answer
741
GATE IT 2006 | Question: 76
x + y/2 = 9 3x + y = 10 The value of the Frobenius norm for the above system of equations is $0.5$ $0.75$ $1.5$ $2.0$
Ishrat Jahan
asked
in
Linear Algebra
Nov 1, 2014
by
Ishrat Jahan
1.5k
views
gateit-2006
linear-algebra
normal
numerical-methods
non-gate
25
votes
8
answers
742
GATE IT 2006 | Question: 26
What are the eigenvalues of the matrix $P$ given below $P= \begin{pmatrix} a &1 &0 \\ 1& a& 1\\ 0&1 &a \end{pmatrix}$ $a, a -√2, a + √2$ $a, a, a$ $0, a, 2a$ $-a, 2a, 2a$
Ishrat Jahan
asked
in
Linear Algebra
Oct 31, 2014
by
Ishrat Jahan
7.4k
views
gateit-2006
linear-algebra
eigen-value
normal
61
votes
8
answers
743
GATE IT 2007 | Question: 2
Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^TAx$ where the maximum is taken over all $x$ that are the unit eigenvectors of $A?$ $5$ $\frac{(5 + √5)}{2}$ $3$ $\frac{(5 - √5)}{2}$
Ishrat Jahan
asked
in
Linear Algebra
Oct 29, 2014
by
Ishrat Jahan
16.2k
views
gateit-2007
linear-algebra
eigen-value
normal
38
votes
7
answers
744
GATE IT 2008 | Question: 29
If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct? S1: Each row of $M$ can be represented as a linear combination of the other rows S2: Each column of $M$ can be represented as a linear combination of the other columns S3 ... solution S4: $M$ has an inverse $S3$ and $S2$ $S1$ and $S4$ $S1$ and $S3$ $S1, S2$ and $S3$
Ishrat Jahan
asked
in
Linear Algebra
Oct 28, 2014
by
Ishrat Jahan
9.6k
views
gateit-2008
linear-algebra
normal
matrix
14
votes
4
answers
745
GATE CSE 1996 | Question: 10
Let $A = \begin{bmatrix} a_{11} && a_{12} \\ a_{21} && a_{22} \end{bmatrix} \text { and } B = \begin{bmatrix} b_{11} && b_{12} \\ b_{21} && b_{22} \end{bmatrix}$ be two matrices such that $AB=I$ ... $CD =I$. Express the elements of $D$ in terms of the elements of $B$.
Kathleen
asked
in
Linear Algebra
Oct 9, 2014
by
Kathleen
4.0k
views
gate1996
linear-algebra
matrix
normal
descriptive
18
votes
4
answers
746
GATE CSE 1996 | Question: 2.6
The matrices $\begin{bmatrix} \cos\theta && -\sin\theta \\ \sin\theta && \cos\theta \end{bmatrix}$ and $\begin{bmatrix} a && 0\\ 0&& b \end{bmatrix}$ commute under multiplication if $a=b \text{ or } \theta = n\pi, n$ an integer always never if $a \cos\theta = b \sin\theta$
Kathleen
asked
in
Linear Algebra
Oct 9, 2014
by
Kathleen
5.3k
views
gate1996
linear-algebra
normal
matrix
48
votes
7
answers
747
GATE CSE 1996 | Question: 1.7
Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknowns. Which of the following is false? The system has a solution if and ... a unique solution. The system will have only a trivial solution when $m=n$, $b$ is the zero vector and $\text{rank}(A) =n$.
Kathleen
asked
in
Linear Algebra
Oct 9, 2014
by
Kathleen
21.3k
views
gate1996
linear-algebra
system-of-equations
normal
12
votes
2
answers
748
GATE CSE 1995 | Question: 2.13
A unit vector perpendicular to both the vectors $a=2i-3j+k$ and $b=i+j-2k$ is: $\frac{1}{\sqrt{3}} (i+j+k)$ $\frac{1}{3} (i+j-k)$ $\frac{1}{3} (i-j-k)$ $\frac{1}{\sqrt{3}} (i+j-k)$
Kathleen
asked
in
Linear Algebra
Oct 8, 2014
by
Kathleen
4.1k
views
gate1995
linear-algebra
normal
vector-space
23
votes
7
answers
749
GATE CSE 1995 | Question: 1.24
The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ ... $1$ $2$ $n$ Depends on the value of $a$
Kathleen
asked
in
Linear Algebra
Oct 8, 2014
by
Kathleen
5.0k
views
gate1995
linear-algebra
matrix
normal
rank-of-matrix
17
votes
3
answers
750
GATE CSE 1994 | Question: 3.12
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
Kathleen
asked
in
Linear Algebra
Oct 5, 2014
by
Kathleen
4.6k
views
gate1994
linear-algebra
matrix
easy
descriptive
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