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xlalcciax
- 12
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1. Let M(2,R) be the set of all 2 x 2 matrics over R. Give an example of matrices A,B,C in M(2,R) such that AB=AC, but B is not equal to C.
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What have you tried? You have to show some effort before we can provide any help.1. Let M(2,R) be the set of all 2 x 2 matrics over R. Give an example of matrices A,B,C in M(2,R) such that AB=AC, but B is not equal to C.
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What have you tried? You have to show some effort before we can provide any help.
No, what this shows is that if A is invertible (has an inverse), then AB = AC implies that B = C. But you're not given that A is invertible.(A^-1)AB=(A^-1)AC so B=C. This shows that A must have no inverse element.
You mean B and C. See if you can cobble up different matrices B and C so that AB = 0 and AC = 0, but B != C.So A could be
1 0
0 0
because det(a)=1-0=0 so A has no inverse. I dont know what A and B could be.
No, what this shows is that if A is invertible (has an inverse), then AB = AC implies that B = C. But you're not given that A is invertible.
You mean B and C. See if you can cobble up different matrices B and C so that AB = 0 and AC = 0, but B != C.
By 0 I meant the 2 x 2 matrix whose entries are all 0.