Linear algebra(linear transformation)

[chuy52506]

Homework Statement

Let B={[1,1]^T,[1,2]^T} be a basis of R².
Suppose T$$\in$$L(R²,R²) with [T]_B=
|1 2|
|3 4|

Homework Equations

Find T([4,3]^T)

The Attempt at a Solution

I augmenting matrix A such that [A|[T]_B]

 

[HallsofIvy]

Why augmenting? The way you have written that you are just asked to find the matrix product
$$\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\begin{bmatrix}4 \\ 3\end{bmatrix}$$

 

[spamiam]

Remember, the columns in the matrix representation of T are just the image of the basis vectors. That is [T]_B =

$$\left(\begin{array}{cc} | & | \\ T(v_1) & T(v_2) \\ | & | \end{array}\right)$$

Use this and then write (4,3) as a linear combination of the basis vectors.

 

[chuy52506]

then would it be
|1| + |1|
|1|*4 + |2|*3= answer?