Question

Which of the following is the product matrix AB

Answer 1

Answer:

The answer is (B)

Step-by-step explanation:

* At first we must now the dimensions of the matrix AB

- If we have two matrices the first of dimension m × n

 and the other of dimension p × q, the multiplication is

 exist if n = p and the dimension of the answer is m × q

∵ The dimension of matrix A is 3 × 2

∵ The dimension of matrix B is 2 × 2

∴ The dimension of AB will be 3 × 2

* From the answer we have only 2 answers have the same

 dimension, answer B and answer D

- To find each element in AB we will multiply each raw

  in A with each column in B lets do it

∵ 1 × 1 + (-4) × (-2) = 1 + 8 = 9 ⇒ 1st raw , 1st column

∵ 1 × 7 + (-4) × 11 = 7 - 44 = -37 ⇒ 1st raw , 2nd column

∵ (-3) × 1 + 2 × (-2) = -3 - 4= -7 ⇒ 2nd raw , 1st column

∵ (-3) × 7 + 2 × 11 = -21 + 22 = 1 ⇒ 2nd raw , 2nd column

∵ 7 × 1 + (-5) × (-2) = 7 + 10 = 17 ⇒ 3rd raw , 1st column

∵ 7 × 7 + (-5) × 11 = 49 - 55 = -6 ⇒ 3rd raw , 2nd column

* AB = $\left[\begin{array}{ccc}9&-37\\-7&1\\17&-6\end{array}\right]$

* The answer is (B)