Write as a Vector Equality 3a+21=5b , 4b+6=-9a

Problem

{[3*a+21=5*b],[4*b+6=−9*a])

Solution

1. Rearrange the equations to bring all terms involving the variables a and b to the left side and the constant terms to the right side.

3*a−5*b=−21

9*a+4*b=−6

2. Identify the coefficients of the variables a and b to form the column vectors for each variable.

a*([3],[9])

b*([−5],[4])

3. Combine the variable vectors and set them equal to the constant vector formed by the values on the right side of the equations.

a*([3],[9])+b*([−5],[4])=([−21],[−6])

Final Answer

a*([3],[9])+b*([−5],[4])=([−21],[−6])

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