1. Let A be an 3 x 4 matrix, and let B be a 4 x 3 matrix. Which of the four oper
ID: 3145033 • Letter: 1
Question
1. Let A be an 3 x 4 matrix, and let B be a 4 x 3 matrix. Which of the four operations AB, BA. AB A B make sense? O A. AB and BA make sense. O B. BA makes sense. ° C. AB makes sense. 0 D. All of the operations make sense. O E. None of the operations make sense. OFA B and A-B make sense O G. A+B makes sense. 2.Let A be an 3 × 4 matrix, and let B be a 4 × 5 matrix which ofthe four operations AB. BA, A + B. A- B make sense? 0 A, A + B makes scase. ( B. BA makes sense. C. All of the operations make sense. 0 D, AB and BA make sense. O EA+B and A- B make sense. O F. AB makes sense. O G. None of the operations make sense. 3·Let A be an 3x 4 matrix. and let B be a 3× 4 matrix, which of the four operations AB.BA. A + B. A-B make sense? O A. AB makes sense O B. AB and BA make sense. O C. BA makes sense. 0 D. None of the operations make sense. OEA+13 and A-Bmake sense. ° F. All of the operations make sense. O G.A+B makes sense 4. Let A be an 20 x 20 matrix, and let Bbe a 20 x 20 matrix Which of the four operations AB, BA. A+B A- B make sense? O A. AB and BA make sense. B. All of the operations make sense. ° C. BA makes sense. 0 D. None of the operations make sense. OEA+B and A B make sense. OF.A+Bmakes sense. O G. AB makes sense.Explanation / Answer
1. A is 3*4 and B is 4*3. The dimensions of A and B are different. So neither A + B nor A - B make sense. However since number of columns in A = number of rows in B and number of columns in B = number of rows in A, both AB and BA make sense.
The correct answer is A.
2. A is 3*4 and B is 4*5. The dimensions of A and B are different. So neither A + B nor A - B make sense. However since number of columns in A = number of rows in B, AB makes sense. The number of columns in B and the number of rows in A are not same and so Ba does not make sense.
The correct answer is B.
3. A is 3*4 and B is 3*4. Due to the same dimensions, A + B and A - B make sense. However since number of columns in A number of rows in B, AB makes sense. The number of columns in B and the number of rows in A are not same and so BA does not make sense.
The correct answer is E.
4. Here all the lengths are 20. Hence all of A + B, A - B, AB and BA make sense.
The correct answer is B.
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