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Determine the product [ (-4 4 4), (-7 1...

Determine the product `[ (-4 4 4), (-7 1 3) and (5 -3 -1)] [(1 -1 1),(1 -2 -2) and (2 1 3)]` and use it to solve the system of equations `x – y + z = 4, x – 2y – 2z = 9, 2x + y + 3z = 1`

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`[ (-4, 4 ,4), (-7, 1, 3) ,(5, -3 ,-1)] [(1, -1, 1),(1, -2 ,-2), (2, 1 ,3)]`
`[ (-4 +4 +8,4-8+4,-4-8+12), (-7+1+6,7-2+ 3,-7-2+9) ,(5 -3 -2,-5+6-1,5+6-3)] `
`=[ ( 8,0,0), (0,8,0) ,(0,0,8)]=8I `
As `A=[ (-4, 4 ,4), (-7, 1, 3) ,(5, -3 ,-1)]`
` B=[(1, -1, 1),(1, -2 ,-2), (2, 1 ,3)]`
`implies AB=8I`
`implies ABB^(-1)=8IB^(-1)`
`B^(-1)=A/8`
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