Question

1 2 3
2 1 3
2 -2 0
1 0 1

Answer 1

A matrix?

Answer 2

Yes

Answer 3

Let L : R3 -> R4 be a map defined as follows: if x in R3 then L(x) = Ax.
Show that L is a linear map.

Answer 4

@zarkon

Answer 5

@myininaya

Answer 6

So we need to show
\[L(x_1+x_2)=A(x_1+x_2)=Ax_1+Ax_2=L(x_1)+L(x_2)\]
and
\[L(c x_1)=A(c x_1)=c A(x_1)=c L(x_1)\]
where c is a number
and
\[x_1,x_2 \in \mathbb{R}^3\]

Answer 7

ok

Answer 8

\[\text{Let } x_1=(a_1 , a_2, a_3)^t \text{ and let } x_2=(b_1,b_2,b_3)^t \]

Answer 9

So ...I don't know how to do matrices in latex (because I suck)
But I can draw it

Answer 10

that's ok , just type it out like I did