Given a linear transformation, determine matrix A

WK95 · Mar 1, 2014

Homework Statement

Problem statement: L: R^2 to R^2 is a linear transformation with L(1,0) = (1,2) and L(0,1) = (-3,4). Determine the matrix A in M2(R) such that L(x) = Ax for every x in R^2.

Homework Equations

The Attempt at a Solution

What is M_2 supposed to be? Is A supposed to be the matrix that produces those above linear transformations?

shortydeb · Mar 1, 2014

pretty much, yes. can you determine what the matrix is?

Mark44 · Mar 1, 2014

WK95 said:

Homework Statement

Homework Equations

The Attempt at a Solution

What is M_2 supposed to be? Is A supposed to be the matrix that produces those above linear transformations?

M₂(R) is the set of 2 X 2 matrices with elements from the field of real numbers. Other notation I've seen is M_2x2.

kduna · Mar 1, 2014

Once a basis has been specified, each linear transformation has a unique matrix representation. Think about the vectors that they gave you ##L## acting on. Do they form a basis? If so, how would they be linked to the form of the matrix?

Given a linear transformation, determine matrix A

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

Homework Statement

Homework Equations

The Attempt at a Solution

Similar threads