Question 55 - Week 6 Practice

Passage

Let

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

be defined by

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

. Let

A=\begin{bmatrix}a&b&c\\d&e&f\end{bmatrix}

be the matrix representation of

T

with respect to

\beta=\{(1,1,0),(0,1,1),(1,0,1)\}

for the domain and

\gamma=\{(1,1),(1,0)\}

for the codomain. Let

S=\{(x,y,z):x=mz,\ y=nz\}

be the nullspace of

T

Question

What is the value of

d-a

Passage question