
7. (15 pts) For the matrix A= -3 1 2 3 6 -2 - 4 -9 -1 1-7 2 3 -1 5 8 - 4 4 9 0 a) Use your calculator to place the matrix in RREF. b) Find a basis for the Range(A). c) Find a basis for Nul(A).
LarPCalc8 8.1.012 45 points 1. Determine the order of the matrix. 47 15 0 -1 0 3 3 6 7 -3 1 O-15 points LarPCalc8 8.1.020. 2. Write the augmented matrix for the system of linear equations. {Sx 4y-2z 24 -21y +8z -3 8x + O-15 points LarPCalc8 8.1.022 My Nete 3. Write the system of linear equations represented by the augmented matrix. (Use the variables x, y, z, and w, if applicable.) 7 -5-4 3 39 8 O-5 points...
4 1 7 1 -3 4 A = -6 8 0 b= . 5 0 3 6 7 2. What is the matrix P describing the orthogonal projection onto R(A), the column space of A?
(1 point) Compute the determinant of the matrix -1 -2 -4 -6 -7 -7 7 7 A= 0 0 0 0 -4 -5 7 det(A) (1 point) Find the determinant of the matrix 6 A- 6 -9 -7 det(A) (1 point) Find the determinant of the matrix 2 2 -2 B= 1 -1 2 3 -2 det (B)
QUESTION 4. Consider the following matrix: I 8 0 167 A= -7 7 0 [ 0 1 2 (a) Find the rank of A Hence, or otherwise find the nullity of A (c) Hence, or otherwise, is A invertible? (d) Find a basis for the nullspace of A. Prove that this set is a basis. [3 marks] [1 marks [1 marks) (3 marks]
[ 2 4 -2 11 4. (20pts) Consider a matrix A = 3 7 -8 6 and corresponding Col A & Nul A. -2 -5 7 3 Col A is a subspace of Rk and Nul A is a subspace of R'. |(1) Find k and one nonzero-vector in Col A. | (2) Find 1 and one nonzero-vector in Nul A.
) Let A be the following matrix: 13 0 2 0 2 2 0 0 6 (a) Enter its characteristic equation below. Note you must use p as the parameter instead of , and you must enter your answer as a equation, with the equals sign. (b) Enter the eigenvalues of the matrix, including any repetition. For example 16,16,24. 5 (c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each eigenvalue's eigenspace. Build an orthogonal...
Find a basis for the column space of the matrix [-1 3 7 2 0 |1-3 -7 -2 -2 1 Let A = 2 -7 -1 1 1 3 and B 1 -4 -9 -5 -3 -5 5 -6 -11 -9 -1 0 0 0 0 It can be shown that matrix A is row equivalent to matrix B. Find a basis for Col A. 3 7 -2 -7 -4 -11 2 -9 -6 -7 -3 0 1 0 0...
1. Find the Jordan canonical forms of the following matrices 0 0 -1 (c) 7 6-3 (b) 2 3 2 1 0 4 0 1 -3 -10-8-6-4 0 -3 1 2 0-1 0 0 0 (d) 2 2 21-1 2 (e) 0-2-5-3 -2 0 6 85 4 0 -5 3-3 -2-3 4
1. Find the Jordan canonical forms of the following matrices 0 0 -1 (c) 7 6-3 (b) 2 3 2 1 0 4 0 1 -3 -10-8-6-4 0...
For the matrix A= 2 4 -7 -8 find a C matrix in the decomposition where A = PCP-1. 3 3 -3 - 31 1/3 -3 1.C= ( 20-6* 2.0-6 c- 3 -3 3 3 4. C= 4 0 -5 V3