Finding unknowns using matrix multiplication

Expand the left-hand side:
Set the resulting matrix equal to the right-hand side:
Now, we can literally just equate the top elements of the left and right-hand matrices, and the bottom elements of the matrices, separately:
Solving the first equation for :
Solving the second equation for :
Both equations give us the same value for , so we can be pretty sure our answer is correct.
Answer:

Expand the left-hand side:
Set the resulting matrix equal to the right-hand side:
Now, we can equate the top elements of the left and right-hand matrices, and the bottom elements of the matrices, separately:
Ah, they’re simultaneous equations! We can solve them using whatever method you like. Here’s substitution, as we know it always works no matter the numbers:
- Rearrange :
- Substitute that value for into the second equation:
- Substitute that value for back into the rearranged first equation:
Answer: and

Expand the left-hand side:
Set the resulting matrix equal to the right-hand side:
Now, we can equate the top-left elements of the left and right-hand matrices, the top-right elements of the matrices, the bottom-left elements of the matrices, and the bottom-right elements of the matrices, separately:
We can rearrange the first two equations to express in terms of :
Set those two expressions for equal to each other:
Substitute that value for back into one of the rearranged equations to find :
Answer: and

Expand the left-hand side:
Set the resulting matrix equal to the right-hand side:
Now, we can equate the top elements of the left and right-hand matrices, the middle elements of the matrices, and the bottom elements of the matrices, separately:
We can rearrange the first two equations to express and in terms of :
Substitute those values for and into the third equation:
Substitute that value for back into the rearranged first two equations:
Answer: , and