c. Evaluate the following determinants: (5 pts) 2 x 2 1. 1 -4 91 | 5...
1. Evaluate the following determinants: 8 7 3 4 0 2 (a) 4 0 1 (c) 6 0 3 6 03 8 2 3 ab (e) b c с a b 1 1 1 2 3 (b) 4 7 5 3 6 9 4 -2 (d) 8 11 4 х (f) 3 9 5 0 y 2 -18 7
1. Evaluate the following determinant. -3 -8 11 7 -2 4 5 6 91
Question 4 5 pts x2 (A) X Ev Evaluate S 0 - 23azdy + cos,+C X (B) -cos-x+C V1-x2 -cos-x+C -r? + cos2x+c (D) - OD B ОА Question 6 5 pts + Evaluate s da. 6V22 +6 A) 3/72 +6 - 3In XV6 (B) 31n x + 12 +6 + c TV +6 2 (C) 22 +6 - 31n|a + v82 +6|+0 (D) xV22 +6 -2.101x + 4x2 +6|+c 2. 12 ОА D B Oc Question 19 5 pts...
Find determinants of the following matrices: 1 5 7 -1 3 2 A= 3 2 8 B= 6 -2 3 C= 6 1 9 7 10 0 13 4 1 0 4 1 -7 2 3 -4 3 D= 4 12 -3 -9 2 6 7 8
cos((+dt. (5 pts.) 1 3. Evaluate the integral 8(t)dt. (5 pts.) 4. Evaluate the sum Σ 23]n]. (4 pts.) 2 +2 +2 + 2+2 4 2
T-1 2 5 ſi 0 0] Q2. (19 pts) Let B 0 1 8 and C = 6 3 0 0 0 1 5 4 1] determinants using the properties of determinants: Compute the following a) det($_35") b) det(3C) c) det(B25) d) det (((3C)B)')
1 2 3 4. (10 pts) Evaluate the determinant of 2 5 3 by (a) cofactor expansion about 1 0 8 column 1 and (b) cofactor expansion about row 3.
(2) Evaluate the following determinants. You may want to use elementary row and/or column operations to reduce the matrix to a simpler form first. 1-1 (a) 1 | 3 -1 2 (b) 1 0 4 -11 1 1 ; 4 2 2 0 5 2 3 0 -1 0 -2 -2 1 -11 (1 2
EXERCISE 5.2 1. Evaluate the following determinants: 2. Determine the signs to be attached to the relevant minors in order to get the following cofactors of a determinant: (C13l, IC23i, (C3sl. Canl, and Cu). 6. Find the minors and cofactors of the third row, given EXERCISE 5.3 4. Test whether the following matrices are nonsingular: EXERCISE 5.4 4. Find the inverse of each of the following matrices: 6. Solve the system Ax=d by matrix inversion, where EXERCISE 5.5 1. Use Cramer's rule to solve the following equation systems: 3. Use Cramer's...
Let A, B and C be 5 x 5-matrices. Assume that the determinants of A, B and C are 3, -3, and -1, respectively What is the determinant of 3 A. (BC 2 Here C equals (C 1) Check your answer