Multiplying matrices with unknowns

[polaris90]

|1 | |4| |0 | |5| |1| |6 |
A|-1 |= |5| ' A |-1|= |3| and A |1|= |8 |
|0 | |0| | 1| |5| |1| |11|

The first question is, determine the dimensions of A. So I can tell it is a 3x3
Then I'm asked to determine the columns of A, I'm not sure about how to to do this.
My attempt was to make A as |a(11) a(12) a(13)|
|a(21) a(22) a(23)|
|a(31) a(32) a(33)|

and multiply it by the first column and set it equal to what's given. The problem is that I will end up with too many unknowns. Can somebody give me a hint, thanks.

 

[tiny-tim]

hi polaris90!

 |1  |   |4|       |0 |   |5|            |1|   |6 |
 A|-1 |= |5| '   A |-1|= |3|     and   A |1|= |8 |
 |0  |   |0|       | 1|   |5|            |1|   |11|

hint: what is A(0,1,0) ?

 

[polaris90]

I'm stuck with this one. I tried multiplying the 3x3 matrix times the matrix given. So fo the first one I got.

|x1 x2 x2| |1| = |-4|
|y1 y2 y3| |-1|= |5|
|z1 z2 z3| |0| = |0|

x1 - x2 = 4
y1 -y2 = 5
z1 - z2 = 0 ==> z1 = z2

I'm not sure what to do after this. I cannot add them up because they have different letter.

 

[DmytriE]

The first matrix that you have written is correct. How about you multiply by the 3x3 matrix that is formed by putting the column vectors on the left side of the equal sign. Then it becomes a straight forward solving linear equations.

 

[tiny-tim]

further hint:

what is A(1,0,0) for any 3x3 matrix A?

and A(0,1,0) ?

and A(0,0,1) ?

now try to make (0,1,0) out of the three vectors given in the question ​