21.3. Matrix Operations

Try these first

1. 1.

   If A = [[2, 4], [6, 8]] and B = [[1, 3], [5, 7]], what is A + B?

   Hint

   Add corresponding elements in the matrices.

2. 2.

   What is the result of performing A - B given A = [[5, 1]] and B = [[2, 4]]?

   Hint

   Subtract the elements of B from A.

3. 3.

   What must be true for matrices A and B to be added?

   • They must have the same dimensions.
   • They must have the same number of elements.
   • They can be of any size.

   Hint

   Think about the definition of matrix addition.

4. 4.

   True or False: Matrix multiplication is commutative.

   • True
   • False

   Hint

   Recall our discussion on matrix multiplication.

5. 5.

   Given matrices A = [[2, 3], [1, 4]] and B = [[6, 5], [7, 2]], calculate A*B. Show all steps of your work.

   Hint

   Follow matrix multiplication rules carefully.

6. 6.

   Prove that if matrix A has a determinant of zero, then it is singular. Provide a detailed explanation.

   Hint

   Reflect on the relationship between determinants and matrix invertibility.