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Recent questions tagged 2-marks
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GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 1
Let $T_{1}, T_{2}: R^{5} \rightarrow R^{3}$ be linear transformations s.t $\operatorname{rank}\left(T_{1}\right)=3$ and nullity $\left(T_{2}\right)=3$. Let $T_{3}: R^{3} \rightarrow R^{3}$ be linear transformation s.t $T_{3}\left(T_{1}\right)=T_{2}$. Then find rank of $T_{3}$
Let $T_{1}, T_{2}: R^{5} \rightarrow R^{3}$ be linear transformations s.t $\operatorname{rank}\left(T_{1}\right)=3$ and nullity $\left(T_{2}\right)=3$. Let $T_{3}: R^{3} ...
GO Classes
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GO Classes
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Apr 11
Linear Algebra
goclasses2025_da_wq1
numerical-answers
linear-algebra
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2
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1
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32
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 4
Let $\mathcal{B}=\left\{\mathbf{b}_{1}, \mathbf{b}_{2}, \mathbf{b}_{3}\right\}$ and $\mathcal{C}=\left\{\mathbf{c}_{1}, \mathbf{c}_{2}, \mathbf{c}_{3}\right\}$ be two bases of $\mathbb{R}^{3}$, and ... $\left[\begin{array}{r}3 \\ -1 \\ 1\end{array}\right]$
Let $\mathcal{B}=\left\{\mathbf{b}_{1}, \mathbf{b}_{2}, \mathbf{b}_{3}\right\}$ and $\mathcal{C}=\left\{\mathbf{c}_{1}, \mathbf{c}_{2}, \mathbf{c}_{3}\right\}$ be two bas...
GO Classes
71
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GO Classes
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Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
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5
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2
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33
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 5
Consider the linear map $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ defined by $ T(x, y)=(x-y, x-2 y), \text { for } x, y \in \mathbb{R} $ Let $\mathcal{E}$ be the standard basis for $\mathbb{R}^{2}$ ... $\left(\begin{array}{ll}0 & -1 \\ 1 & -1\end{array}\right)$
Consider the linear map $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ defined by$$T(x, y)=(x-y, x-2 y), \text { for } x, y \in \mathbb{R}$$Let $\mathcal{E}$ be the stand...
GO Classes
80
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GO Classes
asked
Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
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3
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1
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34
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 6
Suppose that ...
Suppose that$$\left[\left[\begin{array}{l}1 \\2\end{array}\right]\right]_{\mathcal{B}}=\left[\begin{array}{l}3 \\4\end{array}\right] \text { and }\left[\left[\begin{array...
GO Classes
67
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GO Classes
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Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
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4
votes
1
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35
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 7
Consider a $4 \times 4$ matrix $A$ and a vector $\mathbf{v} \in \mathbb{R}^{4}$ such that $A^{4} \mathbf{v}=\mathbf{0}$ but $A^{3} \mathbf{v} \neq \mathbf{0}$ ... $\mathbb{R}^{4}$. $\mathcal{B}$ is a basis of $\mathbb{R}^{4}$. $\mathcal{B}$ is not linearly independent.
Consider a $4 \times 4$ matrix $A$ and a vector $\mathbf{v} \in \mathbb{R}^{4}$ such that $A^{4} \mathbf{v}=\mathbf{0}$ but $A^{3} \mathbf{v} \neq \mathbf{0}$.Set $\mathc...
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85
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GO Classes
asked
Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
multiple-selects
2-marks
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1
votes
1
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36
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 10
Let $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ ... $\left(\begin{array}{lll}2 & 1 & 3 \\ 6 & 3 & 9\end{array}\right)$
Let $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ be a linear transformation such that $T\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right]=\left[\begin{array}{l}2 \\ 6...
GO Classes
64
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GO Classes
asked
Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
2-marks
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3
votes
1
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37
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 11
Which of the following statements are true? There exists a $3 \times 3$ matrix $A$ and vectors $b, c \in \mathbb{R}^{3}$ such that the linear system $A x=b$ has a unique solution but $A x=c$ has infinitely ... $n$, then the column space of $A$ is equal to the column space of $B$.
Which of the following statements are true?There exists a $3 \times 3$ matrix $A$ and vectors $b, c \in \mathbb{R}^{3}$ such that the linear system $A x=b$ has a unique s...
GO Classes
59
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GO Classes
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Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
multiple-selects
2-marks
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2
votes
1
answer
38
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 15
The matrix $ \left(\begin{array}{rr} -2 & 11 \\ 4 & 2 \end{array}\right) $ represents a linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ ... $\left(\begin{array}{rr}-2 & 11 \\ 4 & 2\end{array}\right)$
The matrix$$\left(\begin{array}{rr}-2 & 11 \\4 & 2\end{array}\right)$$represents a linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ with respect to th...
GO Classes
60
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GO Classes
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Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
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