Question 9 - Week 6 Practice | Prasnya

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Week 6

SubjectMathematics 2

Question 9 of 62

Passage question

00:00Est. 2 min

Marks+3.000.00

Passage

Let

T:\mathbb{R}^4\to\mathbb{R}^2

be the linear transformation defined by

T(x_1,x_2,x_3,x_4)=(x_1-x_2,\ x_2-x_3+x_4)

for all

(x_1,x_2,x_3,x_4)\in\mathbb{R}^4

.

Question

Find the value of

k

for which the set

\{(1,1,k^2,k-1),(1,1,0,-1)\}

is a basis for the kernel of

T

.

ComprehensionMedium Difficulty03 August 2025

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