Write as a Vector Equality 8p=12-2q , q+4p=6

Problem

{[8*p=12−2*q],[q+4*p=6])

Solution

1. Rearrange the equations into standard form a*p+b*q=c by moving all variable terms to the left side and constants to the right side.

8*p+2*q=12

4*p+q=6

2. Identify the coefficients of the variables p and q to form the column vectors for each variable.

Vector for *p=[[8],[4]]

Vector for *q=[[2],[1]]

3. Identify the constants on the right side of the equations to form the constant vector.

Constant vector=[[12],[6]]

4. Construct the vector equality by multiplying each variable by its corresponding coefficient vector and setting their sum equal to the constant vector.

p*[[8],[4]]+q*[[2],[1]]=[[12],[6]]

Final Answer

p*[[8],[4]]+q*[[2],[1]]=[[12],[6]]

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