Matrix Power Example-2

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Definition and Examples
Example-2

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2. Example-2

1. Find `A^2` ...
`A=[[2,3],[0,5]]`

Solution:

`A^2`

`A×A`

	`2`	`3`
	`0`	`5`

	`2`	`3`
	`0`	`5`

	`2×2+3×0`	`2×3+3×5`
	`0×2+5×0`	`0×3+5×5`

	`4+0`	`6+15`
	`0+0`	`0+25`

	`4`	`21`
	`0`	`25`

`A^2`

	`2`	`3`
	`0`	`5`

	`4`	`21`
	`0`	`25`

2. Find `A^3` ...
`A=[[2,3],[0,5]]`

Solution:

`A^2`

`A×A`

	`2`	`3`
	`0`	`5`

	`2`	`3`
	`0`	`5`

	`2×2+3×0`	`2×3+3×5`
	`0×2+5×0`	`0×3+5×5`

	`4+0`	`6+15`
	`0+0`	`0+25`

	`4`	`21`
	`0`	`25`

`A^3`

`A^2×A`

	`4`	`21`
	`0`	`25`

	`2`	`3`
	`0`	`5`

	`4×2+21×0`	`4×3+21×5`
	`0×2+25×0`	`0×3+25×5`

	`8+0`	`12+105`
	`0+0`	`0+125`

	`8`	`117`
	`0`	`125`

`A^3`

	`2`	`3`
	`0`	`5`

	`8`	`117`
	`0`	`125`

This material is intended as a summary. Use your textbook for detail explanation.
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