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Recent questions tagged linear-algebra

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Find the value of [v]e wherev is a vector space and e is a list of polynomials

tenjela asked in Mathematical Logic May 17

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1 vote

1 answer

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matrix maths
1 -3 3 0 -5 6 0 -3 4 a 3*3 matrix is given if x,y, z are the eigan value then find xy+yz+ax? my approch if i do row transformation in c2->c2+c3 and then c2->4c2-c3, so my matrix become upper tringular matrix then ... -6 but using genral method via substract lemda from diagonal element and then determinant of matrix getting answer -3 which one is correct and why not other one

jugnu1337 asked in Linear Algebra May 14

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1 answer

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Dknights asked in Linear Algebra Apr 18

142 views

3 votes

1 answer

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GO Classes 2023 | IIITH Mock Test 3 | Question: 5
Number of Linearly independent eigenvectors corresponding to the matrix $ \left(\begin{array}{ccc} 1 & 0 & 0 \\ -2 & 2 & -1 \\ 4 & 0 & 3 \\ \end{array}\right) $ $1$ $2$ $3$ $4$

GO Classes asked in Linear Algebra Apr 15

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0 votes

1 answer

5

#appliedcourse
not getting the answer by 3*3 eigen value formula – (x^3-trace(a)*x^2+sum of minors of a(x)+|a|) eigen values are given as -2,3,6

Dknights asked in Linear Algebra Apr 14

79 views

8 votes

2 answers

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GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 5
Suppose that the characteristic polynomial of $\text{A}$ is $ p(\lambda)=\lambda(\lambda-2)(\lambda-3)^2. $ Which of the following can you determine from this information? The rank of $\text{A}$. Whether $\text{A}$ is symmetric. Whether $\text{A}$ is diagonalizable. The eigenvalues of $\text{A}$.

GO Classes asked in Linear Algebra Apr 5

219 views

6 votes

3 answers

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GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 6
If $\text{A}$ is a $4 \times 3$ matrix and $\text{A} x=b$ is not solvable for some $b$ and the solutions are not unique when they exist, possible values for the rank of $\text{A}$ are ________ (list all possibilities). $0$ $1$ $2$ $3$

GO Classes asked in Linear Algebra Apr 5

228 views

12 votes

1 answer

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GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 7
$A x=b$ has solutions $x_1=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)$ and $x_2=\left(\begin{array}{l}4 \\ 5 \\ 6\end{array}\right)$, and possibly other solutions, for some (real) matrix $A$ and right-hand side $b$. Which of the ... $\left(\begin{array}{l} 4 \\ 4 \\ 4\\ \end{array} \right)$

GO Classes asked in Linear Algebra Apr 5

194 views

8 votes

2 answers

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GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 8
Suppose that $A$ is a $3 \times 3$ real-symmetric matrix with eigenvalues $\lambda_1=1$, $\lambda_2=-1, \lambda_3=-2$, and corresponding eigenvectors $x_1, x_2, x_3.$ You are given that $x_1=\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)$ ... $x_3 =\left(\begin{array}{c} 0 \\ 0 \\ 0 \end{array}\right)$

GO Classes asked in Linear Algebra Apr 5

246 views

11 votes

3 answers

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GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 9
Consider two statements below - Statement $1: $ If $A$ is invertible and $\lambda$ is an eigenvalue of $A$, then $\frac{1}{\lambda}$ is an eigenvalue of $A^{-1}$. Statement $2:$ Let $A$ be a real skew- ... true but Statement $2$ is false Statement $2$ is true but Statement $1$ is false Both statements are true Both statements are false

GO Classes asked in Linear Algebra Apr 5

241 views

6 votes

2 answers

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GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 10
Let $A=\begin{pmatrix}1 & 2 & 1 & 0 & 0 \\ 1 & 2 & 2 & 2 & 3 \\ -1 & -2 & 0 & 2 & 3\end{pmatrix}$ What will be the $\text{rank(A)}?$ $1$ $2$ $3$ $5$

GO Classes asked in Linear Algebra Apr 5

159 views

7 votes

1 answer

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GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 17
You have a matrix $A$ ... $3$ eigenvalues of $A?$

GO Classes asked in Linear Algebra Apr 5

142 views

10 votes

2 answers

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GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 18
In this problem, consider the $4 \times 4$ matrix $A$ whose columns are vectors $\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3, \mathbf{a}_4 \in \mathbb{R}^4$ ... a element in matrix $\text{A}$ at $\mathrm{i}^{\text {th }}$ row and $\mathrm{j}^{\text{th}}$ column.

GO Classes asked in Linear Algebra Apr 5

167 views

12 votes

1 answer

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GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 19
Suppose that we are solving $A x=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)$ In each of the option below, a complete solution $x$ is proposed. Which of the following could possibly be the solution for above system of linear ... $\alpha \in \mathbb{R}$

GO Classes asked in Linear Algebra Apr 5

242 views

15 votes

2 answers

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GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 20
Consider Three matrices $A, B$ and $C$ ... $\alpha_1$, then: The Entries which are not shown in matrices are zeros. What is the rank of $B ?$

GO Classes asked in Linear Algebra Apr 5

271 views

0 votes

0 answers

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GATE EE 2008
Q.51 A is mx n full rank matrix with m>n and I is an identity matrix. Let matrix A' = (A^T.A)^-1 A^T. Then,which one of the following statement is TRUE? (a) AA'A = A (b) (AA)²= A (c) AA'A = I (d) AA'A = A' [EE, GATE-2008, 2 marks] Where, X^T: Transpose of X and X^-1= Inverse of X

Priyanshu Karmakar asked in Linear Algebra Mar 31

by Priyanshu Karmakar

132 views

0 votes

0 answers

17

GATE EE 2007
The linear operation L(x) is defined by the cross product L(x) = b x X, where b=[0 1 0] and X=[xxx]' are three dimensional vectors. The 3 x 3 matrix M of this operation satisfies: L(x)=M (x1 x2 x3)' Then the eigen values of M are: (a) 0, +1,-1 (b) 1, -1, 1 (c) i, -i, 0 (d) i, -i, 1 [EE, GATE-2007, 2 marks]

Priyanshu Karmakar asked in Linear Algebra Mar 30

by Priyanshu Karmakar

66 views

8 votes

2 answers

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GO Classes Weekly Quiz 6 | Linear Algebra | Question: 1
Consider the vectors $\mathbf{v}_1$ and $\mathbf{v}_2$ ... independent otherwise The vectors $\left\{\mathbf{v}_1, \mathbf{v}_2\right\}$ are linearly independent when $t=4$, and linearly dependent otherwise

GO Classes asked in Linear Algebra Mar 29

198 views

7 votes

2 answers

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GO Classes Weekly Quiz 6 | Linear Algebra | Question: 2
Consider a matrix $A_{4 \times 5}$. Where all the solutions of $A x=0$ has the following form - $ \left[\begin{array}{c} 6 c-12 e \\ -4 c+10 e \\ c \\ -5 e \\ e \end{array}\right] $ What will be the rank of $A?$

GO Classes asked in Linear Algebra Mar 29

140 views

12 votes

2 answers

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GO Classes Weekly Quiz 6 | Linear Algebra | Question: 3
Let $A$ be a $n \times n$ matrix, and let $u, v, w$ be nonzero vectors in $\mathbf{R}^n$ which are distinct $(\text{so}\; u \neq v, u \neq w$, and $v \neq w).$ Suppose $A u=2 u, \quad A v=2 v, \quad A w=-w$. Which one of the following vectors must be an eigenvector of $A?$ $u-v$ $v-w$ $u-w$ none of the above

GO Classes asked in Linear Algebra Mar 29

178 views

11 votes

1 answer

21

GO Classes Weekly Quiz 6 | Linear Algebra | Question: 4
Consider a matrix $A_{n \times n}$ having the following characteristic equation - $ \lambda^2(\lambda-3)(\lambda+2)^3(\lambda-4)^3 $ What could be $\operatorname{rank}(\mathrm{A})?$ $6$ $7$ $8$ $9$

GO Classes asked in Linear Algebra Mar 29

164 views

7 votes

1 answer

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GO Classes Weekly Quiz 6 | Linear Algebra | Question: 5
Consider the system below, where $h$ and $k$ are real numbers. $ \begin{array}{r} x+3 y=2 \\ 3 x-h y=k \end{array} $ Find the values of $h$ and $k$ which give the system infinitely many solutions. $h=-9$ and $k \neq 6$ $h \neq-9$ and $k$ can be any real number $h=-9$ and $k=6$ System is inconsistent for all values of $h$ and $k$

GO Classes asked in Linear Algebra Mar 29

92 views

10 votes

1 answer

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GO Classes Weekly Quiz 6 | Linear Algebra | Question: 6
Let $\vec{v}$ be an eigenvector of an invertible matrix $A$. Which of the following are necessarily true? $\vec{v}$ is an eigenvector of $A^{-1}$. $\vec{v}$ is an eigenvector of $A^2$. $\vec{v}$ is an eigenvector of $A+I$. $\vec{v}$ is an eigenvector of $A+2 I$.

GO Classes asked in Linear Algebra Mar 29

172 views

18 votes

1 answer

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GO Classes Weekly Quiz 6 | Linear Algebra | Question: 7
Let $\mathrm{A}$ be a $3 \times 3$ matrix. Let $\mathbf{x}, \mathbf{y}, \mathbf{z}$ are linearly independent $3$ ... $\mathrm{A}$.

GO Classes asked in Linear Algebra Mar 29

260 views

11 votes

2 answers

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GO Classes Weekly Quiz 6 | Linear Algebra | Question: 8
Which of the following is/are TRUE? If the echelon form of an $m \times n$ matrix has a pivot in every column then $n \geq m$ If the echelon form of an $m \times n$ matrix $A$ has a pivot in every row, then ... one solution. If a system of $25$ linear equations in $13$ unknowns has at least one solution then it has infinitely many solutions.

GO Classes asked in Linear Algebra Mar 29

193 views

13 votes

2 answers

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GO Classes Weekly Quiz 6 | Linear Algebra | Question: 9
$ \left[\begin{array}{ll} 3 & 1 \\ 1 & 0 \\ 2 & 5 \end{array}\right]\left[\begin{array}{lll} a & 1 & 0 \\ 2 & b & 1 \end{array}\right]=A_{3 \times 3} $ At what values of $(a, b), A_{3 \times 3}$ will be invertible? $(1,-1)$ $(-1,1)$ Both A and B None of the above

GO Classes asked in Linear Algebra Mar 29

161 views

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Recent questions tagged linear-algebra