4. Classify the null space of each of the following matrices as either a line or a plane: [1 2 3] [1 0 1 0] A= 0 0 2 B= 0 1 0 1 Lo o 1] LO 0 0 0 0 0 1] _ 0 -1 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
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 ()...
linear algebra 1. Consider the following matrices 01 and B=[3 0 4 3 A=[-1 2 O Show that (BA) A-1B-1
Add these two matrices Matrix A= 4 1-2 Matrix B= 1 4 1-2 3 11
A 2 -3 4 1 0 -7 B 6 2 -4 3 5 2 Two matrices are given A and B. What is 2A +3B WHAT IS AB^T
2. Compute the determinant of the following matrices. (a) 2 -1 2 5 -4 A= 3 -11 9 0 (b) 1 2 1 2 1 A= -1 -1 2 1 1 2 (apply row reductions combined with cofactor expansion)
Given the following matrices, find 2A + 3B. 3 2 4 7 A= 1 2 -1 B= 2 -3 a b For the resulting matrix 2 A+3B = where с d a = = C= d
Factor the following matrices into LU form 2 -3 1-3 (b) 2 2 2
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...