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Recent questions tagged linear-algebra

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Engineering mathematics
If A is a non-zero column matrix of order n×1 and B is a non-zero row matrix of order 1×n then rank of AB equals ? Rank(ab) can be zero???

GateOverflow04 asked in Linear Algebra Sep 21

by GateOverflow04

71 views

2 votes

2 answers

2

Made Easy: Linear Algebra (MSQ)
Let $A$ be a $3$ x $3$ matrix with rank $2$. Then, $AX=0$ has The trivial solution $X=0$. One independent solution. Two independent solution. Three independent solution.

DebSujit asked in Linear Algebra Sep 19

147 views

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3

Linear Algebra
MX = O is a homogeneous equation and such an equation when |M| = 0 has non trivial solution. M: Square Matrix O: Null Matrix Kindly help me with the above statement.

ryandany07 asked in Mathematical Logic Aug 30

77 views

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1 answer

4

ISI 2020 | PCB Mathematics | Question: 3
Suppose $A$ is an $(n \times n)$ matrix over $\mathbb{R}$ such that $A^{p}=0$ for some positive integer $p$. Prove that $I+A$ is an invertible matrix, where $I$ is the $(n \times n)$ identity matrix. Find the characteristic polynomial of $A$.

Lakshman Patel RJIT asked in Linear Algebra Aug 8

by Lakshman Patel RJIT

41 views

1 vote

1 answer

5

GATE-2014 EC
Which one of the following statements is NOT true for a square matrix A? If A is real symmetric, the eigen values of A are the diagonal elements of it. If all the principal minors of A are positive, all the eigen values of A are also positive. My question is what is “principal minors of A” ?

samarpita asked in Linear Algebra May 9

180 views

1 vote

1 answer

6

Eigen Values of an orthogonal matrix will always be +1 and the modulus will also be always |1|?
Eigen Values of an orthogonal matrix will always be +1 and the modulus will also be always |1|? I have a doubt on this point .

samarpita asked in Linear Algebra May 9

925 views

5 votes

2 answers

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GATE CSE 2022 | Question: 10
Consider the following two statements with respect to the matrices $\textit{A}_{m \times n}, \textit{B}_{n \times m}, \textit{C}_{n \times n}$ and $ \textit{D}_{n \times n}.$ Statement $1: tr \text{(AB)} = tr \text{(BA)}$ ... $2$ is correct. Both Statement $1$ and Statement $2$ are correct. Both Statement $1$ and Statement $2$ are wrong.

Arjun asked in Linear Algebra Feb 15

by Arjun

1.6k views

5 votes

3 answers

8

GATE CSE 2022 | Question: 35
Consider solving the following system of simultaneous equations using $\text{LU}$ decomposition. $x_{1} + x_{2} - 2x_{3} = 4$ $x_{1} + 3x_{2} - x_{3} = 7$ $2x_{1} + x_{2} - 5x_{3} = 7$ where $\textit{L}$ and $\textit{U}$ ... $\textit{L}_{32}= - \frac{1}{2}, \textit{U}_{33}= - \frac{1}{2}, x_{1}= 0$

Arjun asked in Linear Algebra Feb 15

by Arjun

1.5k views

2 votes

1 answer

9

GATE CSE 2022 | Question: 43
Which of the following is/are the eigenvector(s) for the matrix given below? $\begin{pmatrix} - 9 & - 6 & - 2 & - 4 \\ - 8 & - 6 & - 3 & - 1 \\ 20 & 15 & 8 & 5 \\ 32 & 21 & 7 & 12 \end{pmatrix}$ ... $\begin{pmatrix} - 1 \\ 0 \\ 2 \\ 2 \end{pmatrix}$ $\begin{pmatrix} 0 \\ 1 \\ - 3 \\ 0 \end{pmatrix}$

Arjun asked in Linear Algebra Feb 15

by Arjun

1.5k views

0 votes

0 answers

10

(Solved now) Gateoverflow test doubt
In this question – https://gateoverflow.in/348646/Gate-overflow-linear-algebra-1-10 for $A=\begin{bmatrix} 0 & i\\ -i& 0 \end{bmatrix}$ how is (B) valid ?

o asked in Linear Algebra Jan 31

by o

206 views

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Recent questions tagged linear-algebra