Consider the following matrices.𝐴 = [1 −2 30 1 0] , 𝐵 = [1 0 10 2 11 2 2] , 𝐶 = [1 0 11 2 0−1 1 −1]For each of the following operations, determine whether or not the operation is defined. If it is defined,calculate its value. If it is not defined, explain why not(a) 5𝐴 (b) 𝐴 + 𝐵 (c) 𝐴𝐵 (d) 𝐵𝐴(e) 3𝐵 − 𝐶 (f) 𝐴𝑇𝐶𝑇 (g) 𝐶𝑇𝐴𝑇 (h) (𝐴𝐶)𝑇

Which matrix operation is NOT commutative? a. Matrix inversion b. Matrix subtraction c. Matrix multiplication d. Matrix addition

Which of the following is true for matrices?Question 1Select one: (𝐴𝑇) = 𝐴 (𝐴𝐵)-1 = 𝐵-1𝐴-1 𝐴*𝐼 = 𝐴𝐴𝐵=𝐵𝐴

1. For a non-zero integer which of the following is not defined?(a) a ÷ 0 (b) 0 ÷ a (c) a ÷ 1 (d) 1 ÷ a2. [(– 8) × ( – 3)] × (– 4) is not equal to :(a) (– 8) × [(– 3) × (– 4)] (b) [(– 8) × (– 4)] × (– 3)(c) [(– 3) (– 8)] × (– 4) (d) ( – 8) × (– 3) – (– 8) × (– 4)3. (– 11) × 7 is not equal to(a) 11 × (– 7) (b) – (11 × 7) (c) (– 11) × (– 7) (d) 7 × (– 11)4. The value of [(−4)×(−9)×(−25)]÷[(−2)×(−3)×(−5)] is(a) 12 (b) −30 (c) 40 (d) 305. Which of the following statements is INCORRECT?(a) The multiplicative identity for integers is 1.(b) Subtraction does not obey commutative law in integers.(c) Multiplication of two integers with unlike signs is always positive.(d) Multiplicative inverse of integer a is .1𝑎6. Assertion (A) (-3) ✕ (2) = -6Reason (R) Of the two integers, if one is negative, then their product must be positive.(a) Both A and R are true and R is the correct explanation of A.(b) Both A and R are true but R is not the correct explanation of A.(c) A is true but R is false.(d) A is false but R is true.7. Fill in the blanks:(i) -88 ÷ ____ = 11 (ii) 84 ÷ ____ = 12(iii) ____ ÷ -5 = 25 (iv) ____ 156 = -156×(v) (8)×(−7) = ____ (vi) (−12)×(−7) = ____8. The product of two integers is -2700. If one of them is 25, find the other integer.9. An elevator descends into a mine shaft at the rate of 8 m/min. If the descent starts from 12 m above theground level; how long will it take to reach −468 m?10. Ryan was playing a game where catching a fish in the basket adds 10 points to his score. If hecatches an octopus instead, he loses 5 points. What is his total if he catches 3 fish and 5 octopus?11. A diver needs to descend to a depth of 100 feet. She wants to do it in 5 equal descents.(i) Use the number line to find how far the diver should travel in each of the 5 descents.(ii) To solve this problem, you can set up a division problem: _____.−100? =12. Show that:−5 (12 + 7) = (-5 12) + (-5 7)× ×13. The fish in the pond below, carry somenumbers. Choose any 4 pairs and carry out fourmultiplications with those numbers. Now,choose four other pairs and carry out divisionswith these numbers.For example,1. (–13) × (–15) = 1952. (−24) ÷ 9 = −8314. Allen’s score in a video game was changed by -75 points because he missed some targets. He got -15points for each missed target. How many targets did he miss?15. Ned took a test with 25 questions. He lost 4 points for each of the 6 questions he got wrong andearned an additional 10 points for answering a bonus question correctly. How many points did Nedreceive or lose overall?16 Use the sign >, <, or = in the following: (Show all the steps of your calculations)(i) _______80 + 69 − 319 − 219 − 100 + 70 + 79(ii) __________19 + (− 40) − 37 32 + (− 66) − (− 39)

Consider the matrices and  .Calculate .

9.Question 9Matrix multiplication works if its two operands1 pointare vectors; specifically, the first one is a column vector and the second one is a row vector of any length.are scalars. are square matrices of the same size.The first and second options are correct.The second and third options are correct.All of the options are correct.