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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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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