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Recent questions tagged linear-algebra
4
votes
2
answers
181
TIFR CSE 2023 | Part B | Question: 5
Consider unit vectors $\mathbf{a}$ and $\mathbf{b}$ in $\mathbb{R}^{n}$. Let $\mathbf{w}$ be an arbitrary vector in $\mathbb{R}^{n}$ and $\eta$ be a positive real number such that \[ \mathbf{a}^{\mathbf{T}} \mathbf{b} \geq \eta>0 \geq \ ... $\text{(S3)}$ must be true, but statement $\text{(S2)}$ may be false. Statement $\text{(S1)}$ may be false.
admin
asked
in
Linear Algebra
Mar 14, 2023
by
admin
365
views
tifr2023
linear-algebra
vector-space
4
votes
0
answers
182
TIFR CSE 2023 | Part A | Question: 1
Let $A$ be a symmetric $3 \times 3$ matrix with real entries. Let $u$ and $v$ be non-zero vectors with real entries such that $A u=2 u$ and $A v=3 v$. From the set of values $\{0,1,-1\}$, which values can the inner product $u^{T} v$ take? $0$ only $1$ only $-1$ only All of the values $0,1$ and $-1$ None of the values $0,1$ and $-1$
admin
asked
in
Linear Algebra
Mar 14, 2023
by
admin
491
views
tifr2023
linear-algebra
vector-space
4
votes
1
answer
183
TIFR CSE 2023 | Part A | Question: 3
$A$ is an $n \times n$ matrix with real-valued entries. Further, there exists a vector $x \neq 0$ such that $A x=0$. Now consider a given vector $b$ in $\mathbb{R}^{n}$. How many possible vectors $z$ exist, so that $A z=b?$ $0$ $1$ $n-1$ $n$ Either $0$ or infinite
admin
asked
in
Linear Algebra
Mar 14, 2023
by
admin
423
views
tifr2023
linear-algebra
vector-space
3
votes
1
answer
184
TIFR CSE 2023 | Part A | Question: 5
Suppose $A$ is a $2 \times 2$ matrix such that the sum of the principal diagonal entries of $A$ is $10$ and the sum of the principal diagonal entries of $A^{2}$ is $20$. (For any $2 \times 2$ matrix $B$, the ... $80$ Nonzero, but cannot be uniquely determined from the above data. Cannot be uniquely determined from the above data, and could also be zero.
admin
asked
in
Linear Algebra
Mar 14, 2023
by
admin
301
views
tifr2023
linear-algebra
matrix
4
votes
1
answer
185
TIFR CSE 2023 | Part A | Question: 15
Consider the $n \times n$ matrix $M$ ... $S$ have? $1$ $\left(\begin{array}{l}n \\ 2\end{array}\right)$ $n$ ! $(n !)^{2}$ $n$
admin
asked
in
Linear Algebra
Mar 14, 2023
by
admin
513
views
tifr2023
linear-algebra
matrix
0
votes
0
answers
186
LU decomposition
Use LU Decomposition method to solve the following system. $\left\{\begin{matrix} & x_{1} +x_{2}-x_{3} =1 \\ & x_{1} +2x_{2}-2x_{3} =0 \\ & -2x_{1} +x_{2}+x_{3} =1 \end{matrix}\right.$ ...
kidussss
asked
in
Linear Algebra
Mar 8, 2023
by
kidussss
351
views
linear-algebra
engineering-mathematics
0
votes
0
answers
187
Numerical Method Analysis : Help...
Solve the following system using Gauss elimination with partial pivoting. $\left\{\begin{matrix} &2x_{1}+x_{2}+x_{3}=10\\ & 3x_{1}+2x_{2}+3x_{3}=18 \\ & 5x_{1}+4x_{2}+2x_{3}=9 \end{matrix}\right.$ ...
kidussss
asked
in
Linear Algebra
Mar 8, 2023
by
kidussss
230
views
linear-algebra
engineering-mathematics
17
votes
4
answers
188
GATE CSE 2023 | Question: 8
Let \[ A=\left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{array}\right] \] and \[ B=\left[\begin{array}{llll} 3 & 4 & ... $\operatorname{det}(B)=-\operatorname{det}(A)$ $\operatorname{det}(A)=0$ $\operatorname{det}(A B)=\operatorname{det}(A)+\operatorname{det}(B)$
admin
asked
in
Linear Algebra
Feb 15, 2023
by
admin
11.0k
views
gatecse-2023
linear-algebra
determinant
1-mark
easy
8
votes
4
answers
189
GATE CSE 2023 | Question: 20
Let $A$ be the adjacency matrix of the graph with vertices $\{1,2,3,4,5\}.$ Let $\lambda_{1}, \lambda_{2}, \lambda_{3}, \lambda_{4}$, and $\lambda_{5}$ be the five eigenvalues of $A$. Note that these eigenvalues need not be distinct. The value of $\lambda_{1}+\lambda_{2}+\lambda_{3}+\lambda_{4}+\lambda_{5}=$____________
admin
asked
in
Linear Algebra
Feb 15, 2023
by
admin
12.6k
views
gatecse-2023
linear-algebra
eigen-value
numerical-answers
1-mark
3
votes
1
answer
190
GATE CSE 2023 | Memory Based Question: 13
Let $ A=\left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{array}\right] $ ... $\operatorname{det} \mathrm{B}=-\operatorname{det} \mathrm{A}$ $\operatorname{det} \mathrm{A}=\operatorname{det} \mathrm{B}$
GO Classes
asked
in
Linear Algebra
Feb 6, 2023
by
GO Classes
2.3k
views
memorybased-gatecse2023
goclasses
linear-algebra
determinant
0
votes
0
answers
191
Linear Algebra, Vectors
What is the equation of the plane that contains point (-2, 4, 5) and the vector (7, 0, -6) is normal to the plane? And check if this plane intersects the y-axis.
kidussss
asked
in
Linear Algebra
Jan 13, 2023
by
kidussss
302
views
linear-algebra
engineering-mathematics
vector-space
0
votes
0
answers
192
Linear Algebra, Vectors
Find equation of a line passes through the points = (0, 1, 2) and = (-1, 1, 1).
kidussss
asked
in
Linear Algebra
Jan 13, 2023
by
kidussss
288
views
linear-algebra
engineering-mathematics
0
votes
0
answers
193
Self Doubt
Question: How NullSpace of the matrix A and the uniqueness of the solution of Ax=b are related ??
lalitver10
asked
in
Linear Algebra
Dec 24, 2022
by
lalitver10
292
views
self-doubt
linear-algebra
1
vote
1
answer
194
DRDO CSE 2022 Paper 1 | Question: 1
Compute $\left[M M^{T}\right]^{-1}$ for an orthogonal matrix where \[M=\left[\begin{array}{lll} \frac{1}{\sqrt{2}} & \frac{2}{\sqrt{2}} & \frac{-2}{\sqrt{2}} \\ \frac{-2}{\sqrt{2}} & \frac{2}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{2}{\sqrt{2}} & \frac{1}{\sqrt{2}} & \frac{2}{\sqrt{2}} \end{array}\right] .\]
admin
asked
in
Linear Algebra
Dec 15, 2022
by
admin
436
views
drdocse-2022-paper1
linear-algebra
matrix
3-marks
descriptive
1
vote
0
answers
195
DRDO CSE 2022 Paper 1 | Question: 2
Calculate the eigenvalues of matrix $M, M^{-1}, M^{2}$ and $M+2 I$ where \[M=\left[\begin{array}{cc} 4 & 5 \\ 2 & -5 \end{array}\right].\]
admin
asked
in
Linear Algebra
Dec 15, 2022
by
admin
223
views
drdocse-2022-paper1
linear-algebra
eigen-value
5-marks
descriptive
1
vote
1
answer
196
DRDO CSE 2022 Paper 1 | Question: 3
With no unique solution, solve for $n$ with the following system of equations $\begin{array}{r} a+b+2 c=3 \\ a+2 b+3 c=4 \\ a+4 b+n c=6 \end{array}$
admin
asked
in
Linear Algebra
Dec 15, 2022
by
admin
265
views
drdocse-2022-paper1
linear-algebra
system-of-equations
5-marks
descriptive
0
votes
1
answer
197
MADEEASY TESTSERIES
To justify the OPTION B they gave an example of 2*2 matrix. However we can see that row 2 is linearly dependent on row1. Even though the 2nd row looks non-zero it can be made into zero. SO am I wrong or the explanation is wrong?
DAWID15
asked
in
Linear Algebra
Dec 9, 2022
by
DAWID15
615
views
made-easy-test-series
matrix
linear-algebra
0
votes
0
answers
198
#LinearAlgebra
Is this correct?
robinofautumn
asked
in
Linear Algebra
Nov 24, 2022
by
robinofautumn
337
views
linear-algebra
eigen-value
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