Question 50 - Week 6 Practice | Prasnya

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Week 6

SubjectMathematics 2

Question 50 of 62

Passage question

00:00Est. 2 min

Marks+2.000.00

Passage

Consider

T:\mathbb{R}^3\to\mathbb{R}^2

and

S:\mathbb{R}^2\to\mathbb{R}^3

given by

T(x,y,z)=(x+y,y+z)

and

S(x,y)=(x,y,x+y)

. Let

\beta

and

\gamma

be the standard ordered bases of

\mathbb{R}^3

and

\mathbb{R}^2

.

Question

If

K=\{(x,y,z): ax+by=0,\ cy+dz=0\}

is the null space of

S\circ T

, find

\frac{a}{b}-2\frac{c}{d}

.

ComprehensionMedium Difficulty20 November 2022

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