Multiply the Matrices

Problem

[[√(,7),0],[2,√(,28)]]*[[2√(,3),−√(,7)],[0,−6]]

Solution

1. Simplify the radical √(,28) in the first matrix to make calculations easier.

√(,28)=√(,4⋅7)=2√(,7)

2. Set up the matrix multiplication by multiplying the rows of the first matrix by the columns of the second matrix.

[[(√(,7))*(2√(,3))+(0)*(0),(√(,7))*(−√(,7))+(0)*(−6)],[(2)*(2√(,3))+(2√(,7))*(0),(2)*(−√(,7))+(2√(,7))*(−6)]]

3. Calculate the product for the first row, first column entry.

(√(,7))*(2√(,3))+0=2√(,21)

4. Calculate the product for the first row, second column entry.

(√(,7))*(−√(,7))+0=−7

5. Calculate the product for the second row, first column entry.

(2)*(2√(,3))+0=4√(,3)

6. Calculate the product for the second row, second column entry.

(2)*(−√(,7))+(2√(,7))*(−6)=−2√(,7)−12√(,7)=−14√(,7)

Final Answer

[[√(,7),0],[2,√(,28)]]*[[2√(,3),−√(,7)],[0,−6]]=[[2√(,21),−7],[4√(,3),−14√(,7)]]

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