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).
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"
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