Answer to Question #198364 in Linear Algebra for Zinzi

Question #198364

Suppose that A,B,C and D are matrices with the following sizes: A(5×2),B(4×2),C(4×5),D(4×5)


Determine in each of the following case whether a product is defined.if is it so give the size of the resulting matrix.


i. DC.

ii. -CA+B.

iii. CD-D


5.3 Assume that A and B are matrices of the same size.Determine an expression for A if 2A-B=5(A+2B).


1
Expert's answer
2021-05-25T18:27:31-0400

Step 1

We can add or subtract only matrices of same order. The product AB is possible only if the number of columns of A equals the number of rows of B.


Step 2

Given that,

A is a 5x2 matrix.

B is a 4x2 matrix.

C is a 4x5 matrix.

D is a 4x5 matrix.

(i) The product DC is not possible because, D has 5 columns and C has 4 rows.

(ii) The product CA is possible because C has 5 columns and has 5 rows. Thus, CA is a 4x2 matrix. Hence, -CA+B is possible.

(iii) The product CD is not possible because C has 5 columns and D has 4 rows. Hence, CD-D is not possible.


Given that,

2A−B=5(2A+B)

⇒2A−B=10A+5B

⇒2A−10A=5B+B

⇒−8A=6B

⇒A="\\frac{-6}{8}B =\\frac{-3}{4}B"


Thus, A="\\frac{-3}{4}B"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS