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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 3
Let the $n \times n$ matrix $A$ have an eigenvalue $\lambda$ with corresponding eigenvector $v$. Which of the following statements are true for matrix $A$. $-v$ is an eigenvector of $-A$ with eigenvalue $- \lambda$. If $v$ is also ... $A+B$. eigenvalue of $A^3$ is $\lambda^3$ and the eigenvector is $v^3$ .
Let the $n \times n$ matrix $A$ have an eigenvalue $\lambda$ with corresponding eigenvector $v$.Which of the following statements are true for matrix $A$.$-v$ is an eigen...
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Linear Algebra
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 4
Consider the following matrix A: $\left[\begin{array}{lll}2 & -1 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 2\end{array}\right]$ Which of the following regarding the matrix $A$ ... $x$ is the eigenvector corresponding to eigenvalue $\lambda$ of $A$ then $x$ is also the eigenvector of $A^{-1}$.
Consider the following matrix A:$\left[\begin{array}{lll}2 & -1 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 2\end{array}\right]$Which of the following regarding the matrix $A$ is/are cor...
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Linear Algebra
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 5
Suppose a $3 \times 5$ matrix $A$ has rank $r = 3$. Then the equation $Ax = b$ $\textbf{BLANK 1}$ has $\textbf{BLANK 2}$ ... BLANK 2: Infinitely many solutions BLANK 1: Sometimes, BLANK 2: Unique solution BLANK 1: Sometimes, BLANK 2: Infinitely many solutions
Suppose a $3 \times 5$ matrix $A$ has rank $r = 3$. Then the equation $Ax = b$ $\textbf{BLANK 1}$ has $\textbf{BLANK 2}$.Which of the following are appropriate words ...
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Linear Algebra
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 6
Which of the following statements is/are $\textbf{NOT CORRECT}$? If $v1$ and $v2$ are linearly independent eigenvectors then they can correspond to the same eigenvalue. If $A$ is a nilpotent matrix, meaning that $A^k = 0$ for the ... is an eigenvalue of an invertible matrix $A$ then $\lambda ^{-1}$ is an eigenvalue of $A^{-1}$.
Which of the following statements is/are $\textbf{NOT CORRECT}$?If $v1$ and $v2$ are linearly independent eigenvectors then they can correspond to the same eigenvalue.If ...
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Linear Algebra
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 7
Given an $m \times n$ matrix $A$ whose rows are linearly independent. Now, consider following statements regarding $A$: $S1:$ The system of equations $Ax = b$ for any $b$ is consistent. $S2:$ $Ax = b$ always has a unique solution. ... $S2$ is FALSE. $S1$ is FALSE and $S2$ is TRUE. Both $S1$ and $S2$ are FALSE.
Given an $m \times n$ matrix $A$ whose rows are linearly independent. Now, consider following statements regarding $A$: $S1:$ The system of equations $Ax = b$ for any ...
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Linear Algebra
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 8
Which of the following statements is/are $\textbf{FALSE}$? For $n \times n$ real-symmetric matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvalues. For $n \times n$ matrices $A$ and $B$ with $B$ ... eigenvectors. For $n \times n$ real-symmetric matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvectors.
Which of the following statements is/are $\textbf{FALSE}$?For $n \times n$ real-symmetric matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvalues.For $n \tim...
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