Systems of Equations and Inequalities: Matrices and Determinants

think icon Think & Click: Can Two Matrices Be Multiplied?

Now, you try. Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

Matrix F is 2x3 and matrix G is 3x6. Can you find F times G? What will the dimensions of result be? Can you find G times F? What will the dimensions of the result be?
 

You can find F times G. A 2x3 times a 3x6 will result in a 2x6. You cannot find G times F. You cannot multiply a 3x6 times a 2x3 because the inner dimensions are not equal.
 

Matrix X = row one is 1, 3, negative 2 and 4 and matrix Y = row one is 0, 3, row two is negative 1, 16, row three is negative 7, 0, and row four is 0, 71. Can you find X times Y? What will the dimensions of the result be?
 

You can multiply a 1x4 matrix times a 4x2 matrix. The result will be a 1x2 matrix.