SOLUTION: The cost of six shirts and 2 pairs of trousers is 1320. While that of 3 shirts and 4 pairs of trousers is 1290. Find using a matrix method the cost of 2 shirts and 2 pairs of trou

Algebra ->  Matrices-and-determiminant -> SOLUTION: The cost of six shirts and 2 pairs of trousers is 1320. While that of 3 shirts and 4 pairs of trousers is 1290. Find using a matrix method the cost of 2 shirts and 2 pairs of trou      Log On


   

Question 359550: The cost of six shirts and 2 pairs of trousers is 1320. While that of 3 shirts and 4 pairs of trousers is 1290. Find using a matrix method the cost of 2 shirts and 2 pairs of trousers.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let S be the cost of the shirt, T the trousers.
6S%2B2T=1320
3S%2B4T=1290
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[A]=%28matrix%282%2C2%2C6%2C2%2C3%2C4%29%29
[x]=%28matrix%282%2C1%2CS%2CT%29%29
[b]=%28matrix%282%2C1%2C1320%2C1290%29%29
[A][x]=[b]
[x]=[A]inv[b]
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det[A]=18
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[A]inv=%281%2F18%29%2A%28matrix%282%2C2%2C4%2C-2%2C-3%2C6%29%29
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[x]=%28matrix%282%2C1%2CS%2CT%29%29=%28matrix%282%2C1%2C150%2C210%29%29
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So then 2 shirts and 2 trousers would be
P=2S%2B2T=2%28150%29%2B2%28210%29=300%2B420=highlight%28720%29