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Webpage for Linear Algebra
Recent questions tagged linear-algebra
4
votes
2
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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.
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 ...
admin
371
views
admin
asked
Mar 14, 2023
Linear Algebra
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 $-1$
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 val...
admin
502
views
admin
asked
Mar 14, 2023
Linear Algebra
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
$A$ 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 $\mathbb{R}^{n}$. ...
admin
430
views
admin
asked
Mar 14, 2023
Linear Algebra
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.
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 $20$. ...
admin
305
views
admin
asked
Mar 14, 2023
Linear Algebra
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? $1$ $\left(\begin{array}{l}n \\ 2\end{array}\right)$ $n$ ! $(n !)^{2}$ $n$
Consider the $n \times n$ matrix $M$ defined as follows:$$M=\left(\begin{array}{cccc}1 & 2 & \ldots & n \\n+1 & n+2 & \ldots & 2 n \\2 n+1 & 2 n+2 & \ldots & 3 n \\\vdots...
admin
521
views
admin
asked
Mar 14, 2023
Linear Algebra
tifr2023
linear-algebra
matrix
+
–
0
votes
0
answers
186
LU decomposition
Use LU Decomposition method to solve the following system. $\left\{\begin{matrix} & x_{1} +x_{2}-x_{3} =1 \\ & x_{1} +2x_{2}-2x_{3} =0 \\ & -2x_{1} +x_{2}+x_{3} =1 \end{matrix}\right.$ ...
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{ma...
kidussss
361
views
kidussss
asked
Mar 7, 2023
Linear Algebra
linear-algebra
engineering-mathematics
+
–
0
votes
0
answers
187
Numerical Method Analysis : Help...
Solve the following system using Gauss elimination with partial pivoting. $\left\{\begin{matrix} &2x_{1}+x_{2}+x_{3}=10\\ & 3x_{1}+2x_{2}+3x_{3}=18 \\ & 5x_{1}+4x_{2}+2x_{3}=9 \end{matrix}\right.$ ...
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_{...
kidussss
234
views
kidussss
asked
Mar 7, 2023
Linear Algebra
linear-algebra
engineering-mathematics
+
–
19
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 & ... $\operatorname{det}(B)=-\operatorname{det}(A)$ $\operatorname{det}(A)=0$ $\operatorname{det}(A B)=\operatorname{det}(A)+\operatorname{det}(B)$
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 & 1 & 2 \\4 & 1 & 2...
admin
11.1k
views
admin
asked
Feb 15, 2023
Linear Algebra
gatecse-2023
linear-algebra
determinant
1-mark
easy
+
–
9
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 $\lambda_{1}+\lambda_{2}+\lambda_{3}+\lambda_{4}+\lambda_{5}=$____________
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 eigenva...
admin
12.7k
views
admin
asked
Feb 15, 2023
Linear Algebra
gatecse-2023
linear-algebra
eigen-value
numerical-answers
1-mark
+
–
4
votes
2
answers
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] $ ... $\operatorname{det} \mathrm{B}=-\operatorname{det} \mathrm{A}$ $\operatorname{det} \mathrm{A}=\operatorname{det} \mathrm{B}$
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 & 1 & 2 \\4 & 1 & 2...
GO Classes
2.4k
views
GO Classes
asked
Feb 5, 2023
Linear Algebra
memorybased-gatecse2023
goclasses
linear-algebra
determinant
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–
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.
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
306
views
kidussss
asked
Jan 13, 2023
Linear Algebra
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).
Find equation of a line passes through the points = (0, 1, 2) and = (-1, 1, 1).
kidussss
291
views
kidussss
asked
Jan 13, 2023
Linear Algebra
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 ??
Question: How NullSpace of the matrix A and the uniqueness of the solution of Ax=b are related ??
lalitver10
295
views
lalitver10
asked
Dec 24, 2022
Linear Algebra
self-doubt
linear-algebra
+
–
1
votes
1
answer
194
DRDO CSE 2022 Paper 1 | Question: 1
Compute $\left[M M^{T}\right]^{-1}$ for an orthogonal matrix where \[M=\left[\begin{array}{lll} \frac{1}{\sqrt{2}} & \frac{2}{\sqrt{2}} & \frac{-2}{\sqrt{2}} \\ \frac{-2}{\sqrt{2}} & \frac{2}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{2}{\sqrt{2}} & \frac{1}{\sqrt{2}} & \frac{2}{\sqrt{2}} \end{array}\right] .\]
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}{\s...
admin
439
views
admin
asked
Dec 15, 2022
Linear Algebra
drdocse-2022-paper1
linear-algebra
matrix
3-marks
descriptive
+
–
1
votes
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 \[M=\left[\begin{array}{cc} 4 & 5 \\ 2 & -5 \end{array}\right].\]
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
225
views
admin
asked
Dec 15, 2022
Linear Algebra
drdocse-2022-paper1
linear-algebra
eigen-value
5-marks
descriptive
+
–
1
votes
1
answer
196
DRDO CSE 2022 Paper 1 | Question: 3
With no unique solution, solve for $n$ with the following system of equations $\begin{array}{r} a+b+2 c=3 \\ a+2 b+3 c=4 \\ a+4 b+n c=6 \end{array}$
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
268
views
admin
asked
Dec 15, 2022
Linear Algebra
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?
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 ...
DAWID15
634
views
DAWID15
asked
Dec 9, 2022
Linear Algebra
made-easy-test-series
matrix
linear-algebra
+
–
0
votes
0
answers
198
#LinearAlgebra
Is this correct?
Is this correct?
robinofautumn
340
views
robinofautumn
asked
Nov 24, 2022
Linear Algebra
linear-algebra
eigen-value
+
–
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