9. 1×1
11. 2×4
13. 2×3
15. a13=3, a31=9, a33=11, a34=12
17. No, it is not a rectangular array of numbers.
19. [214−321]
21. [5−13−7171119]
23. ⎡⎣⎢⎢−1242−3−539−681632⎤⎦⎥⎥
25. ⎧⎩⎨⎪⎪x−2x3x+−−2y3y3y−++3zz2z===457
27. {x2x−+yy+−z3z==26
29. [102131]
31. ⎡⎣⎢1002103514−3−1⎤⎦⎥
33. [4554−7−2]14R1−→−−⎡⎣15544−74−2⎤⎦−5R1+R2→R2−→−−−−−−−−−−−−⎡⎣⎢⎢1054−94−74274⎤⎦⎥⎥−49R2−→−−−⎡⎣10541−74−3⎤⎦
35. ⎡⎣⎢1004−373−2510−3⎤⎦⎥−13R2−→−−−⎡⎣⎢⎢⎢100417323510−3⎤⎦⎥⎥⎥−7R2+R3→R3−→−−−−−−−−−−−−⎡⎣⎢⎢⎢⎢⎢1004173231310−3⎤⎦⎥⎥⎥⎥⎥3R3−→−⎡⎣⎢⎢⎢100410323110−9⎤⎦⎥⎥⎥
37. No, because Property 2 is not satisfied
39. The matrix is in reduced row-echelon form because Properties 1–4 are satisfied.
41. The matrix is in reduced row-echelon form because Properties 1–4 are satisfied.
43. The matrix is in reduced row-echelon form because Properties 1–4 are satisfied.
45. (5,−2); {x+2yy==1−2
47. (−4−4y, y, 3); {x+4y+2zz==23
49. (1, 2,−1); ⎧⎩⎨⎪⎪x+2yy+−3z2zz===24−1
51. (2,−5,−2w+3, w); ⎧⎩⎨⎪⎪xyz+2w===2−53
53. (−5, 4, 3, 0); ⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪xyz+2ww====−5430
55. {(5,−3)}
57. {(3, 1)}
59. {(−15,−2325)}
61. {(2, 1)}
63. {(1, 2, 3)}
65. {(2, 3, 4)}
67. {(1, 2, 3)}
69. {(52, 32, 72)}
71. {(1+4z, 3−3z, z)}
73. {(1, 2,−1)}
75.
One solution
Infinitely many solutions
No solution
77. False. Each row of A has seven entries.