Calculate the following products and sums or give reasons why they are not defined

Chapter 7, Problem 7.1.19

(choose chapter or problem)

Let

\(\mathbf{A}=\left[\begin{array}{rrr}6 & -2 & -2 \\10 & -3 & 1 \\-10 & 5 & 1\end{array}\right], \quad \mathbf{B}=\left[\begin{array}{rrr}9 & 4 & -4 \\4 & 7 & 0 \\-4 & 0 & 11\end{array}\right]\)

\(\mathbf{C}=\left[\begin{array}{rr}3 & 1 \\0 & -2 \\4 & 0\end{array}\right], \quad \mathbf{a}=\left[\begin{array}{l}5 \\1 \\2\end{array}\right], \quad \mathbf{b}=\left[\begin{array}{lll}

3 & 0 & 8\end{array}\right]\)

Calculate the following products and sums or give reasons why they are not defined. (Show all intermediate results.)

\(\mathbf{A B}, \mathbf{B} \mathbf{A}, \mathbf{A} \mathbf{A}^{\top}, \mathbf{A}^{\top} \mathbf{A}\)

Text Transcription:

A = [6  -2  -2 \\10  -3  1 \\-10  5  1],     B = [{9  4  -4 \\4  7  0 \\-4  0  11]

C = [3  1 \\0  -2 \\4  0],     a = [{5 \\1 \\2],     b = [3  0  8]

AB, BA, A A^{T}, A^{T}A}