IITM BS Question 28 - Week 6 Practice

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IITM BS Question 28 - Week 6 Practice | Prasnya

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Q28Comprehension3 Marks30 Apr 2023

Passage

Let

D

denote the set of all

2 \times 2

diagonal matrices. Consider an ordered basis

\beta = \left\{ \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 0 \\ 0 & 2 \end{bmatrix} \right\}

. Let

T: D \to \mathbb{R}^2

be a linear transformation defined as

T\left(\begin{bmatrix} a & 0 \\ 0 & b \end{bmatrix}\right) = (a+b, 4a-5b)

. Let matrix

A

be the matrix representation of

T

with respect to the ordered basis

\beta

for

D

and the standard ordered basis for the co-domain

\mathbb{R}^2

. Answer the given subquestions.

Which of the following is/are true about T?

Q28

00:00

30 Apr 2023

Mathematics 2 · Week 6

Q28.Which of the following is/are true about T?@passage

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