1. Let A Idef g h i Given that det(A) 1, find det(B) where You should...
(1 point) a b c Given det d e f = 5, find the following determinants. g h i g h i det a b c de f. a b c 6f + c 6d + a 6e + b 6f + c = g h i 6d + a 6e + b 6f+c d e f = J
Question B 7. (a) Let -1 0 0 (i) Find a unitary matrix U such that M-UDU where D is a diagonal matrix. 10 marks] (i) Compute the Frobenius norm of M, i.e., where (A, B) = trace(B·A). [4 marks] 3 marks] (iii) What is NM-illp? (b) Let H be an n × n complex matrix (6) What does it mean to say that H is positive semidefinite. (il) Show that H is positive semidefinite and Hermitian if and only...
3. Let det(A) = 3 and det B = –2. Find the indicated determinants: (a) det(AB) (b) det(B-1A) (c) det(AAT) (d) det(3BT)
Гa b c] Let A = d e f . Assume that det(A) = -11, find Igni Ta gol (a) det(2A) (b) det(A-1) c) det(3A-1) (a) det((3A) – 1) (e) detone (a) det(2A) = Click here to enter or edit your answer - 22 (b) det (A-1) = Click here to enter or edit your answer (c) det(3A-1) = Click here to enter or edit your answer (d) det((3A)-1) = Click here to enter or edit your answer a gol...
Exercice 2. Let A given by -(iii) 21 A 1 -2 01 -2 1. Compate det( A) and ine.A) in MATLAB 2Use MATLAB to cheek boy coanpating ine(4)-A and A-inA) 3. Create two 5 x 5 matrices A and B with random entries between -30 and 20 by typing A-round(40 (rand3)-3) Bu40 (rands)-0. We will use these matrices to tind relationship between determinants Use MATLAB to fill the belom table det det (A det(A+B) (A) + det(B) det(AB) det(A det...
9. Given det(A5x5)-3, find det(A3), det(5A), det(2AT), det(3A-1). 9. Given det(A5x5)-3, find det(A3), det(5A), det(2AT), det(3A-1).
18. Let T be the matrix transformation T -1 2 0 -1 2 2 -1 h 2 -3 k 4 a. What are the domain and codomain of T? b. Find the REF of [T]. Hint: You'll need the REF in some of the following questions. -1 -1 -1 -3 (REF of [7]= 0 2 2 4 is given here so that you can correctly answer the following 0 0 h – 2 k-6 questions.) c. Define the range of...
els response. Let B -- [1 1 L2 2. 0 1 31 2. Find det B 1 (a) via reduction to triangular form (b) by cofactor expansion swer) in the textbox below. Only work on your blank sheets of paper. You will submit your 3 (12pt) - T-
Let H={p() : p()= a + b + cf*: a,b,cer} (a)(3 marks) Show that H is a subspace of P3. (b) Let P1, P2, P3 be polynomials in H, such that Py(t) = 2, P2(t) = 1 +38P3(0)= -1-t-Use coordinate vectors in each of the following and justify your answer each part (1) (5 marks) Verify that {P1, P2, P3} form a linearly independent set in P3- (11) (2 marks) Verify that {P1, P2, P3} does not span P3. (111)...
a. 4. Let h(x) = x4 – 6x3 + 12x2. Find h'(x) and h"(x). b. Find the open intervals on which h is concave upward and concave downward. Give the points of inflection for h as ordered pairs. c. a. 5. Let g(x) = x4 – 2x3 + 3. x3 This function is defined, differentiable, for all real numbers except x = where g has a vertical asymptote. b. Find g'(x), given any other value of x. c. Suppose we...