Match the vector subspaces of \mathbb{R}^3 (with the usual scalar multiplication and vector addition) in column A with their bases in column B and the dimensions of the vector spaces in column C in Table : M2ES2. | | Vector space (Column A) | | Basis (Column B) | | Dimension of the vector space (Column C) | |---|---|---|---|---|---| | a) | W = {(x,y,z) \mid x - y + z = 0, x + y = 0, x,y,z \in \mathbb{R}} | 1) | {(0,1,0),(0,0,1)} | i) | 1 | | b) | W = {(x,y,z) \mid x = 0, x,y,z \in \mathbb{R}} | 2) | {(1,0,0),(1,1,0),(1,1,1)} | ii) | 3 | | c) | W = Span{(1,2,1),(2,1,3),(0,6,-2)} | 3) | {(-1,1,2)} | iii) | 2 | | d) | W = Span{(1,2,1),(2,1,3),(3,3,3)} | 4) | {(1,5,0),(0,-3,1)} | iv) | 2 | Table : M2ES2

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Mathematics for Data Science II · End Term · 8 Aug 2021 · May 2021 term

Question 6: Match the vector subspaces of \mathbb{R}^3 (with the usua…

Question 6

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Match the vector subspaces of $\mathbb{R}^3$ (with the usual scalar multiplication and vector addition) in column A with their bases in column B and the dimensions of the vector spaces in column C in Table : M2ES2.

	Vector space (Column A)		Basis (Column B)		Dimension of the vector space (Column C)
a)	$W = \{(x,y,z) \mid x - y + z = 0, x + y = 0, x,y,z \in \mathbb{R}\}$	1)	$\{(0,1,0),(0,0,1)\}$	i)	1
b)	$W = \{(x,y,z) \mid x = 0, x,y,z \in \mathbb{R}\}$	2)	$\{(1,0,0),(1,1,0),(1,1,1)\}$	ii)	3
c)	$W = Span\{(1,2,1),(2,1,3),(0,6,-2)\}$	3)	$\{(-1,1,2)\}$	iii)	2
d)	$W = Span\{(1,2,1),(2,1,3),(3,3,3)\}$	4)	$\{(1,5,0),(0,-3,1)\}$	iv)	2

Table : M2ES2

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Question 6 of 12 in the IIT Madras BS Mathematics for Data Science II (Maths 2) End Term paper sat on 8 Aug 2021, in the May 2021 term (IIT M TERM FINAL EXAM POD21TEANQP2 8 Aug 2021). It carries 5 marks.

Question 6: Match the vector subspaces of \mathbb{R}^3 (with the usua…

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