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

Problem

[[a,b],[c,d]]*[[2,2],[0,2]]=[[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.

[[a(2)+b(0),a(2)+b(2)],[c(2)+d(0),c(2)+d(2)]]=[[6,2],[4,2]]

2. Simplify the expressions within the resulting matrix.

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

3. Set up a system of equations by equating the corresponding entries of the two matrices.

2*a=6

2*a+2*b=2

2*c=4

2*c+2*d=2

4. Solve for a using the first equation.

a=6/2=3

5. Solve for b by substituting the value of a into the second equation.

2*(3)+2*b=2

6+2*b=2

2*b=−4

b=−2

6. Solve for c using the third equation.

c=4/2=2

7. Solve for d by substituting the value of c into the fourth equation.

2*(2)+2*d=2

4+2*d=2

2*d=−2

d=−1

Final Answer

a=3,b=−2,c=2,d=−1

Want more problems? Check here!