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?
Let A. B, C, D є Mnxn(F), and det(A) 0, AC-CA. Prove that A B det ( )) -det(AD CB)
Question 1 of 8 1.0 Points 11 [100] [o 1 1] , B= 0 1 2 and C = 0 1 2. Which of 10 3 4 10 3 4] Consider the matrices A= 3 4 these matrices is/are invertible? O A. All of them O B. A and B only O C. A and C only OD. B and C only O E. None of them Reset Selection Part 2 of 7 - Question 2 of 8 1.0 Points...
9s 11 (1 pt) Find the inverse Laplace transform f(t) = L=1 {F(s)}| of the function F(s) s2 2s5 9s 11 f(t)= L' help (formulas) $2-2S+5
o 1 0 -1 Exercise 2. Let A= in M3,R, and ✓ = 0 in R3. -1 0 For every vector W E R3, set g(W) = WT AT ER. (i) Show that g: R3 → R defines a linear transformation. What is the matrix [g]C,B in the - 1 bases C = {1} and B { 8.00 } ? (ii) Let f : R3 → R be the function defined by f() = 7T Aw E R. Show that...
dear instructor, please solve question with full explanation. thanks roblem 1. [3.0p] Let u AD, DC, - CB and dicates. Assume that ABCD is a parallelogram with AD parallel to BC. BA, as the figure Explain why AD-BC a. b. Explain why c. Write AC in terms of ü and e. d. Write AC in terms of z and u e. Find the sums i+a, ( +u ) + 6 , and ( (z +a) +6 ) + 0 ,...
Week 7: Nonlinear equations 1. Let f(x) --9. The equation (x)0 has a solution in [0, 1] i) Find the interpolation polynomial that interpolates f at x,-0, x2 1 0.5 and x3-1. ii) Use this polynomial to find an approximation to the solution of the equation f(x)0 Week 7: Nonlinear equations 1. Let f(x) --9. The equation (x)0 has a solution in [0, 1] i) Find the interpolation polynomial that interpolates f at x,-0, x2 1 0.5 and x3-1. ii)...
7. Let S : X Y and B CY. Show that f[f-?[B]] CB and = B if f is surjective. 8. Show that the set of infinite sequences from 0, 1 is not countable. (Hint: Let : N → E. Then f(m) is a sequence < amn>0. Let bm = 1 - amm. Then <b > is a sequence in E and for each k, <br>< akn >= f(k). This is "Cantor's diagonal process".]
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)
1. Let A Idef g h i Given that det(A) 1, find det(B) where You should fully justify your answer 3 marks]