Find the Variables [[6,0],[0,2]][[a,b],[c,d]]=[[6,2],[4,2]]

Problem

[[6,0],[0,2]]*[[a,b],[c,d]]=[[6,2],[4,2]]

Solution

1. Perform matrix multiplication on the left side by multiplying the rows of the first matrix by the columns of the second matrix.

[[6*(a)+0*(c),6*(b)+0*(d)],[0*(a)+2*(c),0*(b)+2*(d)]]=[[6*a,6*b],[2*c,2*d]]

2. Set up a system of equations by equating the corresponding entries of the resulting matrix to the matrix on the right side.

6*a=6

6*b=2

2*c=4

2*d=2

3. Solve for a by dividing both sides of the first equation by 6

a=1

4. Solve for b by dividing both sides of the second equation by 6 and simplifying the fraction.

b=1/3

5. Solve for c by dividing both sides of the third equation by 2

c=2

6. Solve for d by dividing both sides of the fourth equation by 2

d=1

Final Answer

[[6,0],[0,2]]*[[a,b],[c,d]]=[[6,2],[4,2]]⇒a=1,b=1/3,c=2,d=1

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