Severity [1] 3 1 3 2 3 0 0 0 3 3 2 3 3 1 1 1 2 0 3 3 0 1 2 0 1 3 0 3 0 3 0 3 1 2 2 4 2 [38] 3 1 1 3 3 3 3 2 1 3 3 0 1 2 3 0 3 3 3 0 0 1 3 1 0 3 3 0 1 0 3 1 0 1 3 3 0 [75] 3 3...
1 -3 2 -8 1 -1 2 -2/ 0 -7 and B = 0 0 -3 7 3 -2 0 4 -2 [2 4 3 31 1 1 1 - 2 You are given the matrices, A= 3 2 0 1 possible, calculate the determinant of A + B. O-18 O 30 oo 06 0-5 O Cannot be determined from the given information
3. Consider 2 00 0 0 3 12 A=1-4 3 3-2 -2 21 0 You are given that the characteristic polynomial of A is XA (z) = (z 2). Find the Jordan form J of A and find a matrix P such that P-1AP J. (You do not need to find P-1.) (You may use an online RREF calculator, but remember you only have an ordinary calculator in the exams.)
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?
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 3 -6 9 0 1 -2 0 3. Let A= 2 -4 7 2 The RREF of A iso 0 1 3 -6 6 -6 0 0 0 (a) (6 points) Find a basis for Col A, the column space of A. 0 (b) (2 points) What is rank A? (c) (6 points) Find a basis for Null A, the null space of A. (d) (2 points) What is the dimension of the null space of A?
7. Consider the following matrices 2 3-1 0 1 A=101-2 3 0 0 0-1 2 4 2 3 -1 B-101-2 0 0-1 2 3 -1 0 c=101-2 3 For each matrix, determine (a) The rank. (b) The number of free variables in the solution to the homogeneous system of equa- tions (c) A basis for the column space d) A basis for the null space for matrices A and HB e) Dimension of the column space (f) Nullity (g) Does...
Verify the identity. (3 cos 0-6 sin 0)2 + (6 cos 0+3 sin 0)2 = 45 Choose the sequence of steps below that verifies the identity. O A. (3 cos 0-6 sin 0)2 + (6 cos 0 + 3 sin 0)2 = 9 cos - 36 sin 20 + 36 cos 20+9 sin ?e =9 (cos?0+ sin 20) +36 (cos 20+ sin ?e) = 9+ 36 = 45 O B. (3 cos 0 - 6 sin 0)2 + (6 cos...
Given an f={(-5,4), (-3, – 2), (0, – 3), (-2, 0), (4, - 4)} dg={(-4, -3), (-3, 2), (-2,-5), (0, 1), (4, 3)}, determine (fog)(-2)
Compute the indicated product. 2 -1 0 4 5 2 2 2 3 -3 0 1 0 -1 0 =