the matrix A, the matrix of coefficients, then there's a vector

This matrix that I chose for an example is a good matrix. A non singular matrix. An invertible matrix.

So an identity matrix is a matrix.

Matrix A.

For example, the matrix A above is a 3 2 matrix.

If we call this augmented matrix, matrix A, then I want to get it into the reduced row echelon form of matrix A.

When you take a matrix and you multiply it times each of the column vectors, when you transform each of the column vectors by this matrix, this is the definition of a matrix matrix product.

A 2 by 3 matrix, a 2 by 3 times 3 by 2 matrix, I got a 2 by 2 matrix.

(a) Part 1 of the matrix

This is our definition of matrix matrix products.

Returns the transpose of a matrix, i. e. rows and columns of the matrix are exchanged.

The change of basis matrix is just a matrix with all of these vectors as columns.

problem is the matrix form and using a matrix that I'll call A.

Now by our definition of matrix matrix products, this product right here is going to be equal to the matrix, where we take the matrix A and multiply it by each of the column vectors of this matrix here, of B plus C.

This is our transformation matrix S. This is our matrix A.

We've learned about matrix addition, matrix subtraction, matrix multiplication.

We multiplied the 3 by 2 matrix times a 2 by 3 matrix, and we got a 3 by 3 matrix.

I still have to do a matrix product, but finding the transpose of a matrix is pretty straightforward.

That's my matrix a.

It's a diagonal matrix.

Is there a matrix, where if I were to have the matrix a, and

Well that's just our matrix A times our vector or our matrix uppercase A.

So turn this from a vector, vector dot product to a matrix, matrix product.

It's actually going to be a 3 by 3 matrix, a much bigger matrix.

We can represent it as the sum of two matrix, but it is just a matrix.

So to convert from a matrix of minors to a matrix of cofactors, you just have to remember this pattern.

Matrix multiplication or matrix products with vectors is always a linear transformation.

And by the definition of matrix products, this is going to be equal to the matrix B plus C is just a matrix, right?

So in general, the nullity of any matrix of any matrix

So the inverse of matrix a is equal to 1 over the determinant of a times the adjugate, or adjoint, of matrix a.

Function MDETERM returns the determinant of a given matrix. The matrix must be of type n x n.

The identity matrix times any other matrix is just that matrix.

So the matrix representation of the entire composition is going to be this matrix times this matrix.

In mathematics, an integer matrix is a matrix whose entries are all integers.

Matrix of minors.

But of course, if I multiplied the inverse matrix times the identity matrix, I'll get the inverse matrix.

The trace of a nilpotent matrix is zero.

So this is the adjoint of matrix a.

So my matrix A times.

A times the matrix B.

So this is matrix A.

The definition of matrix products is you take the first matrix and multiply times the column vectors of the second matrix.

So notice, if we called this matrix A and this is matrix B, right?

If we have a 2x2 matrix, the identity matrix is 1, 0, 0, 1.

Let's say I have my matrix B and it is a fairly simple matrix.