Section 2.3

1.
1. (a) F
2. (b) T
3. (c) F
4. (d) T
5. (e) F
6. (f) F
7. (g) F
8. (h) F
9. (i) T
10. (j) T
2.
1. (a) $A (2 B + 3 C) = (\begin{array}{r} 20 & - 9 & 18 \\ 5 & 10 & 8 \end{array})$ $A (2 B + 3 C) = (\begin{array}{r} 20 & - 9 & 18 \\ 5 & 10 & 8 \end{array})$ and $A (B D) = (\begin{array}{r} 29 \\ - 26 \end{array})$ $A (B D) = (\begin{array}{r} 29 \\ - 26 \end{array})$
2. (b) $A^{t} B = (\begin{array}{r} 23 & 19 & 0 \\ 26 & - 1 & 10 \end{array})$ $A^{t} B = (\begin{array}{r} 23 & 19 & 0 \\ 26 & - 1 & 10 \end{array})$ and $C B = (\begin{array}{l} 27 & 7 & 9 \end{array})$ $C B = (\begin{array}{l} 27 & 7 & 9 \end{array})$
3. (a) ${[T]}_{β} = (\begin{array}{r} 2 & 3 & 0 \\ 0 & 3 & 6 \\ 0 & 0 & 4 \end{array}), {[U]}_{β}^{γ} = (\begin{array}{r} 1 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & - 1 & 0 \end{array}),$ ${[T]}_{β} = (\begin{array}{r} 2 & 3 & 0 \\ 0 & 3 & 6 \\ 0 & 0 & 4 \end{array}), {[U]}_{β}^{γ} = (\begin{array}{r} 1 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & - 1 & 0 \end{array}),$ and ${[UT]}_{β}^{γ} = (\begin{array}{r} 2 & 6 & 6 \\ 0 & 0 & 4 \\ 2 & 0 & - 6 \end{array})$ ${[UT]}_{β}^{γ} = (\begin{array}{r} 2 & 6 & 6 \\ 0 & 0 & 4 \\ 2 & 0 & - 6 \end{array})$
4.
1. (a) $(\begin{array}{r} 1 \\ - 1 \\ 4 \\ 6 \end{array})$ $(\begin{array}{r} 1 \\ - 1 \\ 4 \\ 6 \end{array})$
2. (c) (5)
12.
1. (a) No.
2. (b) No.

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Table of Contents for Section 2.3