1.
(a) F
(b) F
(c) T
(d) T
(e) F
(f) T
(g) T
(h) T
(i) T
2.
(a) 2
(c) 2
(e) 3
(g) 1
4. (a) ⎛⎝⎜100010000000⎞⎠⎟; the rank is 2.
5.
(a) The rank is 2, and the inverse is (−112−1).
(c) The rank is 2, and so no inverse exists.
(e) The rank is 3, and the inverse is ⎛⎝⎜⎜⎜⎜⎜⎜1612−16−1301312−1212⎞⎠⎟⎟⎟⎟⎟⎟.
(g) The rank is 4, and the inverse is ⎛⎝⎜⎜⎜−5131−10−315−9317−41112−721⎞⎠⎟⎟⎟.
6.
(a) T−1(ax2+bx+c)=−ax2−(4a+b)x−(10a+2b+c)
(c) T−1(a, b, c)=(16a−13b+12c, 12a−12c, −16+13b+12c)
(e) T−1(a, b, c)=(12a−b+12c)x2+(−12a+12c)x+b
7. ⎛⎝⎜101010001⎞⎠⎟⎛⎝⎜110010001⎞⎠⎟⎛⎝⎜1000−20001⎞⎠⎟⎛⎝⎜100210001⎞⎠⎟⎛⎝⎜10001−1001⎞⎠⎟⎛⎝⎜100010101⎞⎠⎟
20.
(a) ⎛⎝⎜⎜⎜⎜⎜⎜1−2100310−21000000000000000⎞⎠⎟⎟⎟⎟⎟⎟
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