And then, finally, for step four, what we do is multiply by one over the determinant of our original matrix. Then, for step three, we find the adjugate, also known as the adjoint matrix. Step two, we then find the cofactor matrix. So, first of all, if we’re gonna find the inverse, step one is to find the matrix of minors. What we’ll also notice when we’re looking to find the inverse is that a lot of steps that we’ll usually complete will be a lot easier because of this particular matrix we have. And if we can check the form of our inverse, we can see that this is the case, because once again, we have the bottom left three elements as zero. And what we know about an upper triangular matrix is that the inverse of said matrix will also be an upper triangular matrix. So, therefore, the elements that are not zero form a triangle in the top right-hand side. We know this because we look at the elements in the bottom left-hand side, they’re all three zero. Well, the first thing we can notice about our matrix □ is that it is an upper triangular matrix. Find its inverse given that it has the form one, □, □, zero, one, □, zero, zero, one, where □, □, and □ are numbers that you should find. Consider the matrix □ is equal to one, two, three, zero, one, four, zero, zero, one.
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