Find the Variables [[3,5],[0,1]][[a],[b]]=[[8],[-5]]

Problem

[[3,5],[0,1]]*[[a],[b]]=[[8],[−5]]

Solution

1. Perform matrix multiplication on the left side of the equation by multiplying the rows of the first matrix by the column vector.

[[3*a+5*b],[0*a+1*b]]=[[8],[−5]]

2. Set up a system of linear equations by equating the corresponding entries of the resulting vectors.

3*a+5*b=8

b=−5

3. Substitute the value of b into the first equation to solve for a

3*a+5*(−5)=8

4. Simplify the equation and isolate the variable a

3*a−25=8

3*a=33

a=11

Final Answer

a=11,b=−5

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