Mathematics for Data Science II · Quiz 2 · 20 Nov 2022 · September 2022 term

Question 11: Consider a linear transformation T : \mathbb{R}^3 \to \m…

Question 11

+1 markOne correct option

Consider a linear transformation $T : \mathbb{R}^3 \to \mathbb{R}^2$ such that the matrix representation of $T$ is $A = \begin{bmatrix} 1 & -1 & 0 \\ 0 & 2 & 3 \end{bmatrix}$ with respect to the ordered bases $\beta = \{(1,0,0), (0,1,0), (1,1,1)\}$ and $\gamma = \{(1,0), (1,1)\}$ for the domain and codomain, respectively. Answer the subquestions based on the given data.

Which of the following option is true?

A
T is one-one.
B
T is onto.
C
T is an isomorphism.
D
T is neither one-one nor onto.

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Correct answer

B
T is onto.

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Question 11 of 15 in the IIT Madras BS Mathematics for Data Science II (Maths 2) Quiz 2 paper sat on 20 Nov 2022, in the September 2022 term (IIT M FOUNDATION AN2 EXAM QPF1 20 Nov 2022). It carries 1 mark.

Question 11: Consider a linear transformation T : \mathbb{R}^3 \to \m…

Question 11

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