- c.
- d.Statement ais false because you cannot add a real number to a matrix. As for statement b, simplifying
the left side of the equation in choice byields the equivalent equation.
While X = –5 makes the corresponding entries along the diagonals of the two matrices the same, the
entries to their immediate right are not equal. There is no X-value that makes these two matrices equal.
And finally, statement c is false since you cannot subtract two matrices that have different dimensions.- a.Equating corresponding entries reveals that the following three equations must hold simultaneously:
x– 2 = – x^2 ,2y= y^2 , and 4z^2 = 8z. First, solve each equation:
x– 2 = –x^22 y= y^24 z^2 = 8z
x^2 + x– 2 = 0 4 y= y^44 z^2 – 8z= 0
(x+ 2)(x– 1) = 0 y^4 –4y 4 z(z– 2) = 0
x= –2, 1 y(y^3 – 4) = 0 z= 0, 2
y= 0,^34 We must form all combinations ofx,y, and zvalues to form the ordered triples that make the equality
true. There are eight such ordered pairs:(–2, 0, 0), (–2, 0, 2), (–2,^34 , 0), (–2,^34 ,2)(1, 0, 0), (1, 0, 2), (1,^34 , 0), (1,^34 , 2)Set 54 (Page 127)
- b.
- d.The matrix 2Ghas dimensions 34 and the matrix –3Ehas dimensions. 13. Since the inner
dimensions are not equal in the terms of the product, (2G)(–3E), the product is not defined. - c. AB
1
0
1
2
2
1
1
3
2
5
1
0
5
6
4
12
10
3
1
0
1
–
––
––
––
==
R
T
S
S
SS
R
T
S
S
S
S
>
V
X
W
W
WW
V
X
W
W
W
W
H
CF==>>> 10 –^14 HH H^0000
x
x
x
x3
0
0
0
3
3
0
0
0
3
3
0
0
0
3
3
15
0
0
0
1
15
0
0
0
1
15
0
0
0
1
15
––
––
––
–
=
R
T
S
S
S
S
S
R
T
S
S
S
S
S
V
X
W
W
W
W
W
V
X
W
W
W
W
W
=– 9321 C
= 9 ––– (^321) C
=+ 999 ––– (^300) CCC+ 0 20 00 1
32999 –– (^100) CC C–+ 010 00 1
ANSWERS & EXPLANATIONS–