Question

Find ATA and AAT for the following matrix. 4-1-4-6 31 2 -5 4 AAT = What do you observe? This answer has not been graded yet.

Answer 1

A = $\begin{bmatrix} 4 &-6 &3 \\ 2&-5 & 4 \end{bmatrix}$

A^t = $\begin{bmatrix} 4 &2 \\ -6 &-5 \\ 3 & 4 \end{bmatrix}$

A^t * A

$\begin{bmatrix} 4 &2 \\ -6 &-5 \\ 3 & 4 \end{bmatrix}$$\begin{bmatrix} 4 &-6 &3 \\ 2&-5 & 4 \end{bmatrix}$

4-4+22 4(-6) +2-5) 4.3+24 3. 3+4.4 3.4+4 2

A^T A =   $\begin{bmatrix} 20 &-34 &20 \\ -34 &61 &-38 \\ 20 &-38 & 25 \end{bmatrix}$

AA^T $\begin{bmatrix} 4 &-6 &3 \\ 2&-5 & 4 \end{bmatrix}$ $\begin{bmatrix} 4 &2 \\ -6 &-5 \\ 3 & 4 \end{bmatrix}$

2:40017 01 4. 4+(-6) (-6) +3 3 4. 2+(-6) (-5) +3. 4 2. 4+(-5) (-6) +4- 3 2 2+(-5) (-5)+4.4 4-90-

AA^T = $\begin{bmatrix} 61 &50 \\ 50 & 45 \end{bmatrix}$

A^T A matrix is 3x3

and AA^T matrix is 2x2