00:01
Okay, so for this question, we have a system of equation.
00:06
And part a says to write the following system as a matrix equation, ax equals b.
00:14
And so basically, matrix a is just simply the coefficient matrix.
00:20
And so we would just take the coefficients of x and y and put that in a matrix.
00:27
So for the first column, we just take the x coefficients, and so it's 5, and then three.
00:34
And then the next column is just the y coefficients.
00:37
And so that's three and two.
00:39
And then x is just the variables that we have in the system of equations.
00:44
And so we have x and y and then equals b.
00:49
And here b is just what's on the right side of the equation.
00:54
So it would just be four and three.
00:57
And to confirm that this is the right equation that corresponds to this system of equations, we can just multiply these matrices out.
01:05
So then we'd have five times x plus three times y.
01:09
And so that's five x plus three y equals four.
01:13
And then for the second one, it's three x plus two y equals three.
01:18
And so we see that that's exactly what we have here.
01:21
And so then moving on to part b, part b says the inverse of a is what? so we have to remember that for two by two matrices, the inverse is simply 1 over ad minus bc, and d, negative b, negative c, a.
01:40
For a general matrix here, where the entries are a, b, c, d.
01:45
And so using this general form, we can find the inverse of a...