IITM BS Question 6 - Week 6 Practice

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IITM BS Question 6 - Week 6 Practice | Prasnya

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Q6Comprehension3 Marks6 Apr 2026

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Let

T:\mathbb{R}^3\to\mathbb{R}^3

be a linear transformation defined by

T(x,y,z)=(x+y+z,\ x+2y+3z,\ 2x+3y+4z)

. Let

U=\{(x,y,z)\in\mathbb{R}^3\mid x+y+z=0\}

. Define the linear transformation

S=T|_U:U\to\mathbb{R}^3

. Based on the above data, answer the given subquestions.

Consider a vector

v\in U

such that

S(v)\in\operatorname{span}\{(1,1,1)\}

, and

\|v\|^2=6

, where

\|\cdot\|

is the norm with respect to the standard inner product on

\mathbb{R}^3

. Which options are the possible choices for

v

00:00

6 Apr 2026

Mathematics 2 · Week 6

Q6.Consider a vector

v\in U

such that

S(v)\in\operatorname{span}\{(1,1,1)\}

, and

\|v\|^2=6

, where

\|\cdot\|

is the norm with respect to the standard inner product on

\mathbb{R}^3

. Which options are the possible choices for

v

?@passage

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