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linear algebra 1. Consider the following matrices 01 and B=[3 0 4 3 A=[-1 2 O Show that (BA) A-1B-1
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
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...
Use the following matrices A, B, and C to solve the following problems A2 -13 0 -3-2 C -1 31 where c is any constant value c -4 2 0 A) What is B'B? B) What is A3? C) What is (AB)TC? D) Determine if the following operations are possible. You do not need to perform the operations A+C CA AB A+B AC BA
Verify the following properties, using any distinct, invertible A, B, 4×4 upper triangular matrices of your choice: 3. (0.5 marks each) Verify the following properties, using any distinct, invertible A, B, 4 x 4 upper triangular matrices of your choice: (a) The inverse of an upper triangular matrix is upper triangular; (b) (AB)- B-1A-1 (e) trace(AB) trace(BA); (d) det(AB) det (BA) example of matrices A, B such that det(AB) det(BA) (BONUS 1 mark) Give an 3. (0.5 marks each) Verify...
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
Q3 (3 points) Show that if both AB and B A are defined then AB and BA are square matrices. + Drag and drop your images or click to browse... Q4 (3 points) Let A = (a) be a 2 x 2 matrix. The trace of A. which we denote by tr(A) is a number defined as tr(A) = 0 + 0x2. Prove the following properties of this number for 2 x 2 matrices A and B and a real...
Need help!! 1) Let A, B, C, and D be the matrices defined below. Compute the matrix expressions when they are defined; if an expression is undefined, explain why. [2 0-1] [7 -5 A= .B -5 -4 1 C- ,D= (-5 3] [I -3 a) AB b) CD c) DB d) 3C-D e) A+ 2B 2) Let A and B be the matrices defined below. 4 -2 3) A=-3 0, B= 3 5 a) Compute AB using the definition of...
find the eigen space of 4a and 4c Find the characteristic equations of the following matrices 4. (a) 「 4 0 1 -2 1 0 -2 0 1 (b) [3 0-5 1 1-2 11 1-2 0 (c) 19 5 -4 (d) -1 0 11 -1 3 0 -4 13 1 (e) 5 0 11 ind bases for the eigenspaces of the matrices in Exercise 4 6. Find the characteristic equations of the following matrices 4. (a) 「 4 0 1...
3. -4 points 3.2.036. 0/3 Submlssions Used an example to show that if A and 8 are symmetric n x n matrices, then AB need not be symmetric. 1 2 1 0 0 1 0 2 0 1 OA-12 0 1 o] 1 0 0 1 (b) Prove that if A and B are symmetnic n n matrices, then AB is symmetric if and only if AB BA. Suppose A and B are symmetric. Then (AB)T ATs-AB. Thus, AB is...