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

Question 10: Consider a linear transformation T : \mathbb{R}^3 \to \m…

Question 10

+2 marksNumerical answer

Consider a linear transformation T:R3→R2T : \mathbb{R}^3 \to \mathbb{R}^2 such that the matrix representation of TT is A=[1−10023]A = \begin{bmatrix} 1 & -1 & 0 \\ 0 & 2 & 3 \end{bmatrix} with respect to the ordered bases β={(1,0,0),(0,1,0),(1,1,1)}\beta = \{(1,0,0), (0,1,0), (1,1,1)\} and γ={(1,0),(1,1)}\gamma = \{(1,0), (1,1)\} for the domain and codomain, respectively. Answer the subquestions based on the given data.

Nullity of the matrix A is

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Correct answer: 1

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Question 10 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 2 marks.

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