Linear Algebra

Final answer only please!

Section 2.2 Properties of Determinants: Problem 1 (1 point) If A and B are 3 x 3 matrices, det (A) = 2, det (B) = -8, then det (AB) = det (3.A) = det (A]) = det (B 1) = det (B?) =Section 2.2 Properties of Determinants: Problem 2 (1 point) If the determinant of a 4 x 4 matrix A is det (A) = 9, and the matrix B is obtained from A by multiplying the first row by 10, then det (B) =Section 2.2 Properties of Determinants: Problem 3 (1 point) If the determinant of a 4 x 4 matrix A is det (A) = 10, and the matrix O is obtained from A by swapping the second and third columns, then det (C) =Section 2.2 Properties of Determinants: Problem 4 (1 point) If the determinant of a 4 x 4 matrix A is det (A) = 9, and the matrix D is obtained from A by adding 7 times the third row to the second, then det (D) =Section 2.2 Properties of Determinants: Problem 5 (1 point) Suppose that a 4 x 4 matrix A with rows v1, v2, v3, and v4 has determinant det A = -9. Find the following determinants: U1 det U3 AVA U1 det U3 v1 + 8v3 U2 det Us V4Section 2.2 Properties of Determinants: Problem 6 {1 point} If a 4 x 4 matrix Awith rows v1: v3, 1:3: and at has determinant that A = 9. 51.31 51'; 31:1 - Bag -- then det = t t 1);; ' Section 2.2 Properties of Determinants: Problem 7 (1 point) Are the following statements true or false? 2 1. The determinant of A is the product of the diagonal entries in A. 2 v 2. If det (A) is zero, then two rows or two columns are the same, or a row or a column is zero. 2 3. If two row interchanges are made in sucession, then the determinant of the new matrix is equal to the determinant of the original matrix. ? v 4. det(AT) = (-1)det(A). ? True N False to get credit for this problem all answers must be correct.Section 2.2 Properties of Determinants: Problem 8 (1 point) a b C Given det d e f = 2, find the following determinants. g h i g h det ! a b C = e f a b C det -9d + a -getb -9f+c = g h 9d +a -ge+b -9f+c] det d g h\f