# Linear algebra(linear transformation)

## 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|

Find T([4,3]T)

## The Attempt at a Solution

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

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

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.

then would it be
|1| + |1|