Passage question

00:00Est. 3 min

Marks+4.000.00

Passage

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.

Question

Find the dimension of the image of

S

.

ComprehensionMedium Difficulty06 April 2026

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