How would I find a 2x2 matrix to multiply another 2x2 matrix by to get zero if that matrix is not the zero matrix? Specifically I have

[1 2]

[3 4] times B = 0

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- Jul 7th 2007, 06:39 AMCT_Mathmatrix products
How would I find a 2x2 matrix to multiply another 2x2 matrix by to get zero if that matrix is not the zero matrix? Specifically I have

[1 2]

[3 4] times B = 0 - Jul 7th 2007, 06:50 AMJhevon
Let the unknown matrix be

We want:

Thus we need the solution to the systems:

..............(1)

..............(2)

and

....................(1)

...................(2)

Can you take it from here?

(That's the systematic way to do it, but really, as with numbers, multiplying any number by zero gives zero, so too with matrices: any matrix times the zero matrix gives the zero matrix, you will find that the solution to the above systems is a = b = c = d = 0) - Jul 7th 2007, 08:17 AMred_dog
Let . We have , so is invertible. Then multiplying both members at left with , we have

- Jul 7th 2007, 08:18 AMJhevon
- Jul 7th 2007, 02:11 PMtopsquark
- Jul 7th 2007, 02:30 PMJhevon
- Jul 7th 2007, 04:21 PMtopsquark