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4. Use the matlab command inv to find the inverse of the matrix A below. Then adjoin the identity matrix I=eye(3) to A to form the 3x6 matrix B=[A I]. Row-reduce using rref B to find the inverse of a again. What do you observe? \begin{bmatrix} 1 & 2 & -1 \\ 3 & 7 & -10 \\ 7 & 16 & -21 \end{bmatrix} 5. Using the same matrix A from problem 4 above. Find the transpose of the matrix, $A^T$. The command for the transpose of a real matrix A is A'. Find the transpose of the matrix by hand. Does your match with MATLAB? 6. Let A and B be the 3x3 matrices below. \begin{bmatrix} 2 & 4 & \frac{5}{2} \\ -\frac{3}{4} & 2 & \frac{1}{4} \\ \frac{1}{4} & \frac{1}{2} & 2 \end{bmatrix} \begin{bmatrix} 1 & -\frac{1}{2} & \frac{3}{4} \\ \frac{3}{2} & -\frac{1}{2} & -2 \\ \frac{1}{4} & 1 & \frac{1}{2} \end{bmatrix} a. Use MATLAB to find $A^{-1}B^{-1}$, $(AB)^{-1}$, and $(BA)^{-1}$. What do you observe? b. Use MATLAB to find $(A^{-1})^T$ and $(A^T)^{-1}$. What do you observe? Remember: You can obtain answers in rational form by using the rats command.

          4. Use the matlab command inv to find the inverse of the matrix A below. Then adjoin the
identity matrix I=eye(3) to A to form the 3x6 matrix B=[A I]. Row-reduce using rref B to
find the inverse of a again. What do you observe?
\begin{bmatrix} 1 & 2 & -1 \\ 3 & 7 & -10 \\ 7 & 16 & -21 \end{bmatrix}
5. Using the same matrix A from problem 4 above. Find the transpose of the matrix, $A^T$. The
command for the transpose of a real matrix A is A'. Find the transpose of the matrix by hand.
Does your match with MATLAB?
6. Let A and B be the 3x3 matrices below.
\begin{bmatrix} 2 & 4 & \frac{5}{2} \\ -\frac{3}{4} & 2 & \frac{1}{4} \\ \frac{1}{4} & \frac{1}{2} & 2 \end{bmatrix}  \begin{bmatrix} 1 & -\frac{1}{2} & \frac{3}{4} \\ \frac{3}{2} & -\frac{1}{2} & -2 \\ \frac{1}{4} & 1 & \frac{1}{2} \end{bmatrix}
a. Use MATLAB to find $A^{-1}B^{-1}$, $(AB)^{-1}$, and $(BA)^{-1}$. What do you observe?
b. Use MATLAB to find $(A^{-1})^T$ and $(A^T)^{-1}$. What do you observe?
Remember: You can obtain answers in rational form by using the rats command.

4. Use the matlab command inv to find the inverse of the matrix A below. Then adjoin the
identity matrix I=eye(3) to A to form the 3x6 matrix B=[A I]. Row-reduce using rref B to
find the inverse of a again. What do you observe?

< b m a t r i x >

5. Using the same matrix A from problem 4 above. Find the transpose of the matrix, A^T. The
command for the transpose of a real matrix A is A'. Find the transpose of the matrix by hand.
Does your match with MATLAB?
6. Let A and B be the 3x3 matrices below.

< b m a t r i x >

< b m a t r i x >

a. Use MATLAB to find A^-1B^-1, (AB)^-1, and (BA)^-1. What do you observe?
b. Use MATLAB to find (A^-1)^T and (A^T)^-1. What do you observe?
Remember: You can obtain answers in rational form by using the rats command.

Added by Consuelo M.

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