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Express the system of equationskx + 2y = 02x + 4y = 1in matrix form, where k is a real...

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roshan-rox | (Level 1) Valedictorian

Posted May 9, 2013 at 10:36 AM via web

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Express the system of equations
kx + 2y = 0
2x + 4y = 1
in matrix form, where k is a real constant.
Hence, find the values of k for which the system has a unique solution.

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted May 9, 2013 at 11:03 AM (Answer #1)

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Express the system of equations
kx + 2y = 0
2x + 4y = 1

We can write this in matrix form as

`[[k,2],[2,4]][[x],[y]]=[[0],[1]]`

`AX=b`

systen AX=b has unique solution if det(A) is non zero.

`det(A)=|A|=4k-4`

ie.     `4k-4!=0`

`k!=1`

Thus system of equation has unique solution for all value of k ,except 1.

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