det (4) 30 000 0 0 0 2233200 0 0 0 0 0 0 0 0 0 0 0 Question 2 (Each blank is 4 points.) 2 2 2 2 2 0 2 02 0 0 0 0 2 0 2 0 0 0 Let A = 2 2 2 2 2 0 0 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 2 2 0 0 0 0 (a), det(A) (b). det(A) 2020
13 please 8. b. -2 3 0 0 0 0 -1 2 0 0-4 0 3 0-2 0 3 0 0 -2 0 3 0 4 o0-1 6 0 0 1 o 2 6 0 0 -1 6 10. For any positive integer k, prove that det(4t) - de(A)*. 11. Prove that if A is invertible, then den(A-1)- I/der(A) - det(4)- 12. We know in general that A-B丰B-A for two n x n matrices. However, prove that: det(A . B)-det(B...
2 1 -2 3 0 1 4 2 1. Let B -3 0 3 ( 1) 2 2 -1 0 (a) Find det(B).(Show all work.) -3 -R2- .A 4 O0-2/2 1-3 0 3 入ス-1 0 I-2 3 det ao -1 O 3 1-3 RyR-( 2 2-10 420 4 (b) Find det(BT). (c) Find det(B-1). (d) Find det(-B) . (e) Is 0 an eigenvalue of B? (f) Are thè columns of B linearly independent?
3 -5 0 1 0 2 0 0 Consider the matrix A= -1 -1 0 3 1 0 -3 2 Which of the following statements about the determinant of A is true? det(2A) = 2 det A det(-A) = det A O Multiplying any row of Aby -1 does not change det A Interchanging two rows of A does not change det A
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)')
Linear Algebra 0 m 0 0! A 0 0 0 13 2 0 0 0 0 1 0 31 0 5. Given matrices [o 0 t 0] [o 3 To 00h and B= 0 Lo a 0 0 LO where a, h, m.t are any real numbers, (a) (2 points) find det(A) (b) (2 points) find det(B) (c) (2 points) find det(AB) (d) (2 points) find det (24" B-). (Show your work and clearly give reasons to receive full credit)
and Consider the matrices [1 2 3 4] 1 1 1 1 A= lo -1 0 1 14 34 31 17 7777 1 2 3 4 . Which of the B= lo -1 0 1 La 34 35 following is true? det B = - det A det B = det A det B = -7 det A det B = 7 det A
Exercise 1 Let 1 1 2 4 A= -16 2 5 1 2 - 1 0 2 3 loo-1/ and B 1 2 (1 1 -3 -1 2 2 0 / (1) Compute det A. 3 (2 .-1)-(3.0) = 1.(-2) - (0) = -2 (2) Evaluate : det (+(2(342)*)*") (3) Compute det B.
3 2 1 1 2 3 3) Let C- 2 6-1and D 0 5 6 0 09 12 0 a) Find det(C) b) Find det (D) c) Find det (CD) d) Find det(DC)
Let A be the 4 x 4 matrix given by A= [1 1 3 0 0 2 2 3 0 0 3 0 0 0 4 1 0 1 3 0 0 0 2 3 Define matrices D= 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 and U = such that A = D+U. 0 0 0 0 0 0 For each of the following statements, decide whether the statement is true...