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Recent questions tagged goclasses2025_csda_wq5

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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 1
Let $A$ be an $n \times n$ matrix of real or complex numbers. Which of the following statements are equivalent to: the matrix $A$ is invertible ?The columns of $A$ are linearly ... is $x = 0$. The rank of $A$ is $n$.
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 2
Let $M$ be a $2 \times 2$ matrix with the property that the sum of each of the rows and also the sum of each of the columns is the same constant $c$. Which (if any) ... [\begin{array}{l}1 \\ 1 \\ \end{array}\right]$U$V$W$None of the above
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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 ... $A^3$ is $\lambda^3$ and the eigenvector is $v^3$ .
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 4
Consider the following matrix A:$\left[\begin{array}{lll}2 & -1 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 2\end{array}\right]$ ... to eigenvalue $\lambda$ of $A$ then $x$ is also the eigenvector of $A^{-1}$.
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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  $\textbf{BLANK 2}$. ... many solutionsBLANK 1: Sometimes, BLANK 2: Unique solutionBLANK 1: Sometimes, BLANK 2: Infinitely many solutions
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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 ... $A$ then $\lambda ^{-1}$ is an eigenvalue of $A^{-1}$.
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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 $Ax = b$ ... FALSE.$S1$ is FALSE and $S2$ is TRUE.Both $S1$ and $S2$ are FALSE.
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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 ... matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvectors.
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 9
Let $A$ and $B$ be two $n \times n$ matrices. If $B$ is invertible and $(I+BA)^{-1} = 2B^2$, then which of the following is the correct definition of $A$ in terms of $B$ ... $A = 2B^3-I$None of the above
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 10
A $4 \times 4$ matrix $\mathrm{A}$ has rank 3 . Which of the following is/are true?1. $A^{-1}$ does not exist2. $A^{-1}$ may exist, ... less than 5Only 1 is correctOnly 2,3 are correctOnly 4 is correctNone of the statements are correct.
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 11
The rank and nullity of a matrix $A$ are 4 and 2 , respectively. The nullity of $A^{\top}$ is 3 . What are the dimensions of $A$ ?$6 \times 7$4 \times 5$7 \times 6$5 \times 4$
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 12
Consider two matrices $\mathrm{A}_{6 \times 3}$ and $\mathrm{B}_{3 \times 6}$, the non zero eigenvalues(EVs) of matrix $A B$ are $3,2,7,8$; see the following ... and $\mathrm{S} 2$ are trueNeither $\mathrm{S} 1$ nor $\mathrm{S} 2$ is true
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 13
Which of the followings(s) is/are TRUE ?If a system of linear equations has no free variables, then it has a unique solution.If an augmented matrix ... $b$ in the set of real numbers of dimension $m$.
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 14
Which of the following(s) is/are TRUE ?If none of the vectors in the set $S=\left\{\vec{v}_1, \vec{v}_2, \vec{v}_3\right\}$ in $\mathbb{R}^3$ is a multiple ... . Then $\left\{\vec{v}_1, \vec{v}_2, \vec{v}_3\right\}$ is linearly independent.
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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 15
Consider the following two statements:$S 1$. If $A B=I$, then $A$ is invertible.$S 2$. If $A$ is a $3 \times 3$ ... is false$\mathrm{S} 1$ is false but $\mathrm{S} 2$ is trueBoth are trueBoth are false
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