Recent questions tagged goclasses2024_wq7 / GATE Overflow for GATE CSE

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1

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 $\text{A}$.

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?T...

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GO Classes asked Apr 5, 2023

9 votes

4 answers

2

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). $0$ $1$ $2$ $3$

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 $...

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GO Classes asked Apr 5, 2023

14 votes

1 answer

3

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 ... $\left(\begin{array}{l} 4 \\ 4 \\ 4\\ \end{array} \right)$

$A x=b$ 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 solution...

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GO Classes asked Apr 5, 2023

13 votes

2 answers

4

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 $x_1=\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)$ ... $x_3 =\left(\begin{array}{c} 0 \\ 0 \\ 0 \end{array}\right)$

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 ...

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GO Classes asked Apr 5, 2023

13 votes

3 answers

5

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

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...

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GO Classes asked Apr 5, 2023

9 votes

2 answers

6

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 $\text{rank(A)}?$ $1$ $2$ $3$ $5$

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$

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GO Classes asked Apr 5, 2023

11 votes

2 answers

7

GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 13
Consider the following list of $137$ statements: $\left(S_1\right): $ There is exactly $1$ false statement in this list. $\left(S_2\right): $ There are exactly $2$ ... true. It is possible that more than one statement in this list is true. Exactly one statement in this list is true.

Consider the following list of $137$ statements:$\left(S_1\right): $ There is exactly $1$ false statement in this list.$\left(S_2\right): $ There are exactly $2$ false st...

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GO Classes asked Apr 5, 2023

9 votes

1 answer

8

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

You have a matrix $A$ with the factorization:$$A=\underbrace{\left(\begin{array}{ccc}1 & & \\3 & 2 & \\1 & -1 & 2\end{array}\right)}_B \quad \underbrace{\left(\begin{arra...

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GO Classes asked Apr 5, 2023

14 votes

2 answers

9

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.

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=\left[\math...

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GO Classes asked Apr 5, 2023

17 votes

1 answer

10

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 ... $\alpha \in \mathbb{R}$

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 followi...

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GO Classes asked Apr 5, 2023

18 votes

2 answers

11

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 $B ?$

Consider Three matrices $A, B$ and $C$ such that -$$\underbrace{\left(\begin{array}{lllll}1 & 2 & 4 & 2 & 5 \\& 2 & 3 & 5 & 6 \\& & 3 & 4 & 3 \\& & & 4 & 3 \\& & & 5\end{...

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GO Classes asked Apr 5, 2023

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