79. Agriculture A fruit grower raises two crops, apples and peaches. The grower ships each of these crops to three different outlets. In the matrix [125 100 75] A = |100 175 125| a, represents the number of units of crop i that the grower ships to outlet j. The matrix B = [S3.50 $6.00] represents the profit per unit. Find the product RA and state what each entry of the matrix represents.
79. Agriculture A fruit grower raises two crops, apples and peaches. The grower ships each of these crops to three different outlets. In the matrix [125 100 75] A = |100 175 125| a, represents the number of units of crop i that the grower ships to outlet j. The matrix B = [S3.50 $6.00] represents the profit per unit. Find the product RA and state what each entry of the matrix represents.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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#79
![11:36
Done elementary_linear_algebra_8th_...
corresponding two rows of AB are also identical.
1.0
77. Let A and B be n x n matrices. Show that if the ith
row of A has all zero entries, then the ith row of AR
will have all zero entries. Give an example using 2 x 2
matrices to show that the converse is not true.
4
3
27
4
6
3
6.
2
2
1
| -3
78. CAPSTONE Let matrices A and B be of
sizes 3 x 2 and 2 x 2, respectively. Answer each
question and explain your answers.
tement is true when A and B
E
n and c is a scalar.
(a) Is it possible that A = B?
(b) Is A + B defined?
(c) Is AB defined? If so, is it possible that AB = BA?
Tr(B)
d B are square matrices of
BA).
and z such that AR = BA for
79. Agriculture A fruit grower raises two crops, apples
and peaches. The grower ships each of these crops to
three different outlets. In the matrix
| 125 100 75]
100 175 125
A =
atrices below.
aj represents the number of units of crop i that the
grower ships to outlet j. The matrix
B = [S3.50 $6.00]
I B=
[cos B - sin B]
| sin ß cos B]
on has no solution.
represents the profit per unit. Find the product BA and
state what each entry of the matrix represents.
gh Reserved. May nt be opied scanned or duplicated in whole or in part. Dec o electnic righ sme hind party contet may be pressed from the eBok andor oChupteri
od contet dest materially affect the ovall leaning eperience. Cengage Leming eserves the right o emve addsonal content at any time if heguent rights neriction require it
2.1 Exercises
51
A corporation has three factories,
manufactures acoustic guitars and
Block Multiplication In Exercises 83 and 84, perform the
block multiplication of matrices A and B. If matrices
A and B are each partitioned into four submatrices
[An Au and B =
A =LAn A2
the matrix
25]
70
[B, B12
LB1 B]
umber of guitars of type i produced
day. Find the production levels when
es by 20%.
atrix
then you can block multiply A and B, provided the sizes of
the submatrices are such that the matrix multiplications
and additions are defined.
[A, A2[B, B1]
= La, A LB, B
[A,B, + A1„B21
LA„B, + A„B,,
A„B12 + A1„B]
A„B12 + A„B„
%3D
0.1]R
0.1 D
0.8]1
1
0]
To
[1
83. A =0
2
-1
B =
1
j) represents the proportion of the
that changes from party j to party i,
the proportion that remains loyal to
ection to the next. Find and interpret
ith itself.
3
01
[1
5 6
2
4
8
84. A =
-1
B =
2
5 6
3
4
0 -1 |o
matrices show the numbers of
nds) who lived in each region of
in 2010 and 2013. The regional
eparated into three age categories.
sus Bureau)
True or False? In Exercises 85 and 86, determine
whether each statement is true or false. If a statement
is true, give a reason or cite an appropriate statement
from the text. If a statement is false, provide an example
that shows the statement is not true in all cases or cite an
2010](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc074fc7e-4e48-46f1-bfc4-aee6ba4e6262%2F68d96e6b-171f-4bd2-9d52-01517851bcf6%2Fjuzfid9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:11:36
Done elementary_linear_algebra_8th_...
corresponding two rows of AB are also identical.
1.0
77. Let A and B be n x n matrices. Show that if the ith
row of A has all zero entries, then the ith row of AR
will have all zero entries. Give an example using 2 x 2
matrices to show that the converse is not true.
4
3
27
4
6
3
6.
2
2
1
| -3
78. CAPSTONE Let matrices A and B be of
sizes 3 x 2 and 2 x 2, respectively. Answer each
question and explain your answers.
tement is true when A and B
E
n and c is a scalar.
(a) Is it possible that A = B?
(b) Is A + B defined?
(c) Is AB defined? If so, is it possible that AB = BA?
Tr(B)
d B are square matrices of
BA).
and z such that AR = BA for
79. Agriculture A fruit grower raises two crops, apples
and peaches. The grower ships each of these crops to
three different outlets. In the matrix
| 125 100 75]
100 175 125
A =
atrices below.
aj represents the number of units of crop i that the
grower ships to outlet j. The matrix
B = [S3.50 $6.00]
I B=
[cos B - sin B]
| sin ß cos B]
on has no solution.
represents the profit per unit. Find the product BA and
state what each entry of the matrix represents.
gh Reserved. May nt be opied scanned or duplicated in whole or in part. Dec o electnic righ sme hind party contet may be pressed from the eBok andor oChupteri
od contet dest materially affect the ovall leaning eperience. Cengage Leming eserves the right o emve addsonal content at any time if heguent rights neriction require it
2.1 Exercises
51
A corporation has three factories,
manufactures acoustic guitars and
Block Multiplication In Exercises 83 and 84, perform the
block multiplication of matrices A and B. If matrices
A and B are each partitioned into four submatrices
[An Au and B =
A =LAn A2
the matrix
25]
70
[B, B12
LB1 B]
umber of guitars of type i produced
day. Find the production levels when
es by 20%.
atrix
then you can block multiply A and B, provided the sizes of
the submatrices are such that the matrix multiplications
and additions are defined.
[A, A2[B, B1]
= La, A LB, B
[A,B, + A1„B21
LA„B, + A„B,,
A„B12 + A1„B]
A„B12 + A„B„
%3D
0.1]R
0.1 D
0.8]1
1
0]
To
[1
83. A =0
2
-1
B =
1
j) represents the proportion of the
that changes from party j to party i,
the proportion that remains loyal to
ection to the next. Find and interpret
ith itself.
3
01
[1
5 6
2
4
8
84. A =
-1
B =
2
5 6
3
4
0 -1 |o
matrices show the numbers of
nds) who lived in each region of
in 2010 and 2013. The regional
eparated into three age categories.
sus Bureau)
True or False? In Exercises 85 and 86, determine
whether each statement is true or false. If a statement
is true, give a reason or cite an appropriate statement
from the text. If a statement is false, provide an example
that shows the statement is not true in all cases or cite an
2010
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