## Example Questions

### Example Question #1 : Matrices

Evaluate:       Explanation:

This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change. ### Example Question #1 : Matrices What is ?      Explanation:

You can begin by treating this equation just like it was: That is, you can divide both sides by : Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component: Then, simplify: Therefore, ### Example Question #1 : Matrices

If , what is ?      Explanation:

Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of : Now, this means that your equation looks like: This simply means: and or Therefore, ### Example Question #1 : Matrices

Simplify:       Explanation:

Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first: The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.  ### All ACT Math Resources 