By evaluating a determinate find the equation of the line pa

By evaluating a determinate find the equation of the line passing through the points (-4, 7) and (2, 4). Prove that if V and W are both subspace of a vector space U, then the intersection of V and W (denoted V W) is also a subspace of U.

Solution

Points given are (-4,7) (2,4)

first formulate the deterrminant form

| x y 1|

|-4 7 1|

|2 4 1|

=> x(7 *1 - 1*4) -y(-4*1 - 1*2) +1(-4*4 -2*7)=0

=> x(7-4) -y(-4-2) +1(-16-14)=0

=> 3x +6y -30=0

=> x+2y-10=0

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