# Homework Help: Finding solutions to matrices (should be easy)

1. Oct 17, 2011

### Ush

1. The problem statement, all variables and given/known data
Alvin is informed that the homogeneous system of equations AX = 0 has a
one parameter family of solutions given by

X = t[4 3 0]T

By trial and error, he has found that

X = [-1 5 7]T

is a solution to the inhomogenous problem

AX = B

where

B = [3 -2 -5]T

He suspects there are more solutions

a) Is there a solution to AX=B of the form [1 a b]T? If so, what are a and b?
b) Is there a solution to AX=B of the form [c d 1]T? If so, what are c and d?

2. Relevant equations

AX = B
X = BA-1

3. The attempt at a solution

I'm more used to simple matrices such as the following

I just don't know how to apply this concept to this question,

my test is tomorrow, any help would be appreciated =)

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2. Oct 17, 2011

### Staff: Mentor

The second equation above is true if and only if A is invertible.
From the given information, we can say that
$$A t\begin{bmatrix}4\\3\\0\end{bmatrix} + A \begin{bmatrix}-1\\5\\7\end{bmatrix} = \begin{bmatrix}0\\0\\0\end{bmatrix} + \begin{bmatrix}3\\-2\\-5\end{bmatrix}$$
for any value of t.

For a), Is there some particular value of t for which the two vectors on the right add up to <1, a, b>T?
The b part is similar.