For the following multiple choice questions you may give one

For the following multiple choice questions, you may give one (and only one) answer. Select the single best option.

(5 points) Let A be a 4 x 4 matrix with determinant 3. What is the determinant of 2A? (XIII) (a) 48. (b) 3. (c) 6. (d) There is insufficient information to answer the question. (e) 12. (f) 24. (g) 196,608. (5 points) Let A be a 4 x 4 matrix with determinant 3. Let B be the matrix formed from A by subtracting two times the third row from the first row. What is det B? (XIV) (a) -9. (b) 0. (c) 3. (d) -3. (e) 6. (f) -6. (g) There is insufficient information to answer the question.

Solution

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Consider a matrix A (4 X 4)

Now when a matrix is multiplied by a scalar , then each element is multiplied with that scalar.

Therefore for given matrix determinant shall be

(2^4)*3 (Where 4 is the order of the matrix) , and 3 is the value of |A|

Hence solution is 48

Option A

Solution

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