MIDTERM CAL_CLC 02

Calculus – Fall 2021 Midterm Exam – CLC 02 Time: 60 minutes Multiple Choice Questions (2.5 points) 1. (0. 5 points) If two row interchanges are made in succession, then the new determinant (a) equals to the old determinant (b) equals to -1 times the old determinant 2. (0. 5 points) The determinant of A is the product of the pivots in any echelon form U of A , multiplied by (-1)r , Where r is (a) the number of rows of A (b) the number of row interchanges made during row reduction from A to U (c) the number of rows of U (d) the number of row interchanges made during row reduction U to A 3. (0. 5 points) If A is invertible, then det  A  det  A1   1. (a) True (b) False 4. (0. 5 points) A square matrix A   aij  is lower triangular if and only if aij  0 for (a) i  j (b) i  j (c) i  j (d) i  j 5. (0. 5 points) The product of upper triangular matrices is (a) matrix lower triangular matrix (b) upper triangular matrix (c) diagonal Essay question (7.5 points) 1. (2.0 points) Compute BD and DB for the given matrices, if possible.  3 1 7  B  10 1 8 ,    5 2 4 

 1 4 9  D   6 2 1    7 4 7 

2. (1.5 points) Evaluate each of the following for the given matrix

(a) A2 (b) A3

 7 3 A   5 1

(c) det  5A  3. (2.0 points) Determine if the following sets of vectors are linearly independent or linearly dependent v1  1;1; 1; 2  , v2   2; 2;0; 2  and v3   2; 8;3; 1 . 4. (2.0 points) Use the adjoint matrix to compute the inverse of the following matrix 1 1 2  0 2 1  .    2 0 4 