Neal Bhatia
11/10/07
EA1
Assignment #7
1.
#8. 3 rows
#10.
AB=
[1
7
2 14]
AC=
[1
7
2 14]
Therefore, AB=AC, but B does not equal C as given in the problem.
#16.
a.
False. The answer is the definition of matrix multiplication except that the vectors
should not be added; instead they should form a 3x3 matrix.
b.
True. That is the definition of matrix multiplication.
c.
False. The order cannot be switched, since matrix multiplication is not
commutative.
d.
False. As shown in theorem 3, part d, the transpose of a product of matrices equals
the product of their transposes in the reverse order, not the same order, as given
here.
e.
True. This property of transposing is shown in theorem 3, part b.
2.
#4.
A
1
= .25*[8 4 = [
2
1
7 3]
7/4
3/4]
#6.
A
1
= .2*[5
5
= [1
1
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8]
1.4
1.6]
X=A
1
b= [
2
5]
#14.
If (BC)D=0, then a possible solution is if B C=0, since 0*D=0. Then B=C.
3.
#8.
Since the matrix given has 4 pivot positions and is 4x4, according to theorem 8, part c, it must be
invertible.
#14.
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 Fall '07
 Nocedal
 0 m, 10 J, Neal Bhatia

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