Which of the following is the product matrix ab

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 =

* The answer is (B)

b) the dogs need to shift their focus to human scent.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.