Please answer legibly. 73%a 1:12 PM webwork / math133_winter2018 3 13 3: Problem

Question

Please answer legibly.

73%a 1:12 PM webwork / math133_winter2018 3 13 3: Problem 13 Previous Problem List Next 1 -2 -3 6 matrices B and Csuch that AB-AC but B (1 point) Let A- Find two 2x2 C. Note: In order to get credit for this problem all answers must be correct. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email instructor Page generated at 02/06/2018 at 01:07pm EST WeBWorK © 1 996-2016 | theme: math41 ww-version: 2.11 I pg-version: 2.11] The WeBWorK Project

Explanation / Answer

We have A =

1

-2

3

-6

Let B =

b11

b12

b21

b22

and C =

c11

c12

c21

c22

Then AB =

b11-2b21

b12-2b22

3b11-6b21

3b12-6b22

and AC =

c11-2c21

c12-2c22

3c11-6c21

3c12-6c22

Since AB = AC, we have b11-2b21= c11-2c21…(1), b12-2b22= c12-2c22…(2), 3b11-6b21=3c11-6c21…(3) and 3b12-6b22 = 3c12-6c22…(4). It may now be observed that if we divide the 3rd and the 4th equations by 3, then we get b11-2b21= c11-2c21 and b12-2b22= c12-2c22 which are same as the 1st and the 2nd equations.

Now, let us suppose that b11= 1, b21 = 0, b12=2 and b22 =1. Also, let us suppose that c11= 5. Then, since b11-2b21= c11-2c21,we have 1-0 = 5-2c21 or, c21= (5-1)/2 = 4/2 = 2. Further, let us suppose that c12=4. Now, since b12-2b22= c12-2c22, we have 2-2*1 = 4-2c22 or, c22 = 4/2=2. Thus, if B =

1

2

0

1

and C =

5

4

2

2

Then AS = AC =

1

0

3

0

However, B C.

1

-2

3

-6

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