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) | | Bases (Column B) | | Dimension of the vector space (Column C) | |---|---|---|---|---|---| | a) | W = {(x,y,z) \mid x + y + z = 0, x - z = 0, x,y,z \in \mathbb{R}} | 1) | {(1,0,0),(0,0,1)} | i) | 1 | | b) | W = {(x,y,z) \mid y = 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),(0,0,2)} | 3) | {(1,-2,1)} | iii) | 2 | | d) | W = Span{(1,2,1),(2,1,3),(1,-4,3)} | 4) | {(3,0,5),(0,3,-1)} | iv) | 2 | Table : M2ES2

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Mathematics for Data Science II · End Term · 22 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)		Bases (Column B)		Dimension of the vector space (Column C)
a)	$W = \{(x,y,z) \mid x + y + z = 0, x - z = 0, x,y,z \in \mathbb{R}\}$	1)	$\{(1,0,0),(0,0,1)\}$	i)	1
b)	$W = \{(x,y,z) \mid y = 0, x,y,z \in \mathbb{R}\}$	2)	$\{(1,0,0),(1,1,0),(1,1,1)\}$	ii)	3
c)	$W = Span\{(1,2,1),(2,1,3),(0,0,2)\}$	3)	$\{(1,-2,1)\}$	iii)	2
d)	$W = Span\{(1,2,1),(2,1,3),(1,-4,3)\}$	4)	$\{(3,0,5),(0,3,-1)\}$	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 22 Aug 2021, in the May 2021 term (IITM TERM FINAL EXAM POD21TEANQPA 22 Aug 2021). It carries 5 marks.

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

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