3. Consider the matrices 2 0 0 0 2 1 0 0 0 2 00 0 0 2 1 0 0 02 and B- 0 0 2 1 0 0 02 Show that a)...
linear algebra
1. Consider the following matrices 01 and B=[3 0 4 3 A=[-1 2 O Show that (BA) A-1B-1
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B = [
3 −5, 4 −7] C = [ 3 2 −1 ,−3 3 2, 5 −4 −3 ]
(i) Calculate A + B,
(ii) Calculate AB
(iii) Calculate the inverse of B,
(iv) Calculate the determinant of C.
(b) The points P, Q and R have co-ordinates (2, 2, 1), (4, 1, 2)
and (5, −1, 4) respectively.
(i) Show that P Q~ =...
Question 5 15 pts Consider the following matrices: 2 -21 3 0 9 A= -1 1 1 C=0 -6 0 'T 3 5 12 2 5 Find matrix B so that: AB=C
1 00 0 1 0 00 -2 3 0 0 0 1 I = 0 0 0 0 6. (10%) Let matrices A and 0 -4 5 0 1 0 -6 7 0 0 0 1 B=(I+A) (I-A) , please calculate the matrix (I+ B) - o0
1 00 0 1 0 00 -2 3 0 0 0 1 I = 0 0 0 0 6. (10%) Let matrices A and 0 -4 5 0 1 0 -6 7 0...
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...
1 2 0 5 1 2 0 5 0 1. Consider the matrices A-10 0 3 | and B Ξ | 0 0 1 3 01 . Which of the following 0 0 0 1 0 0 0 0 1 statements is truc? a) None of the matrices is in reduced echelon form b) Both A and B are in reduced echelon form c) Only is in reduced echelon form d) Only B is in reduced echelon forım
Consider the product of two matrices A and B of dimensions 4 x 4 as shown below. 0 1 2 3 11 2 3 4 | 0 1 2 3 I 1 0 2 46X2 3 4 5 I 0369 0 0 0 0 I I 14 20 26 32 I - 28 40 52 64 I I 42 60 78 96 I 3 456 1. Write a program to find the product of two matrices. The program should display...
1. Consider the following matrices. A= 1 2 -1 0 3 4 B 2 3-4 5 1 and C= -[-1:] Compute each of the following, if it is defined. If an expression is undefined, explain why. (a) (4 points) A+B (b) (4 points) 2B (c) (4 points) AC (d) (4 points) CB
Consider the following matrices: 1 2 A= 3-4 2 3 B= 3 2 1 1 0 2 C= 2 1 3 -1 1 1 1 4 5 -4 2 5 1 3 4 1 0 1 1 - 2 D= E= F 4 1 31 7 3 2 Find each of the following, if possible. If it is not possible, explain your reasoning. 1 (a) AB (9) BAT (b) BA (h) (A + B) E (C) CD + E ()...
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10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalue of A, and find a corresponding generalized eigenvector Ax c) Write out the general solution of x
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a)...