mooshupork34

05-05-2007, 02:49 PM

If anyone could help me with the following problem, it would be greatly appreciated!

Consider the linear transformation L: M_22 -> R^4 defined by

L\left(

\begin{array}{cc}

a & b \\

c & d

\end{array}

\right) = (-10a - c + 2d, 5a + b - d, -2c + d, 9a + 17b + 2d).

Compute ker(L).

Okay, so far I've put the coefficients into a matrix and row reduced the matrix to get

1st row: 1, 0, 0, 0

2nd row: 0, 1, 0, 0

3rd row: 0, 0, 1, 0

4th row: 0, 0, 0, 1

But I'm unsure of where to go from there.

Consider the linear transformation L: M_22 -> R^4 defined by

L\left(

\begin{array}{cc}

a & b \\

c & d

\end{array}

\right) = (-10a - c + 2d, 5a + b - d, -2c + d, 9a + 17b + 2d).

Compute ker(L).

Okay, so far I've put the coefficients into a matrix and row reduced the matrix to get

1st row: 1, 0, 0, 0

2nd row: 0, 1, 0, 0

3rd row: 0, 0, 1, 0

4th row: 0, 0, 0, 1

But I'm unsure of where to go from there.