Find A- where AB=C andа, а, азb, b, b,C2 C3b, b, b31C1B=& C=1C1 C2 C3|a1 a2 az

Given matrix is B=a1a2a3b1b2b3c1c2c3 and C=c1c2c3b1b2b3a1a2a3. We have to find the A-1 where AB=C.…

Answered: Find A-1 where AB=C and C2 C3 b, b, bz…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Related questions

Question

Find A- where AB=C and
а, а, аз
b, b, b,
C2 C3
b, b, b3
1
C1
B=
& C=
1
C1 C2 C3
|a1 a2 az

Expert Solution

Step 1

Given matrix is $B = (\begin{matrix} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{matrix})$ and $C = (\begin{matrix} c_{1} & c_{2} & c_{3} \\ b_{1} & b_{2} & b_{3} \\ a_{1} & a_{2} & a_{3} \end{matrix})$ .

We have to find the $A^{- 1}$ where $A B = C$ .

Given $A B = C$

Then $A^{- 1} = C B^{- 1}$ .

If we interchange the first row with third row of the matrix $C = (\begin{matrix} c_{1} & c_{2} & c_{3} \\ b_{1} & b_{2} & b_{3} \\ a_{1} & a_{2} & a_{3} \end{matrix})$ , we get

$\begin{array}{rcl} C & = & - (\begin{matrix} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{matrix}) \\ = & - B \end{array}$