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Question

If 2A+B=110112A2B=012101 find A and B

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Solution

2A+B=110112 and 2A4B=024022

2A+B2A+4B=110112024022

5B=10120+410122+2

5B=134110

B=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢15354515150⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

Substitute B=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢15354515150⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ in 2A+B=110112

2A+⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢15354515150⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥=110112

2A=110112⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢15354515150⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

2A=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢1151+350451151+1520⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

2A=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢5155+35455155+152⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

2A=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢45254545652⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

A=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢25152525351⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥


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