2 3 -6 9 0 1 -2 0 3. Let A= 2 -4 7 2 The RREF of A iso 0 1 3 -6 6 -6 0 0 0 (a) (6 points) Find a basis for Col A, the column space of A. 0 (b) (2 points) What is rank A? (c) (6 points) Find a basis for Null A, the null space of A. (d) (2 points) What is the dimension of the null space of A?
Q1. Find a basis and dimension for row space, column space and null space for the matrix, -2 - 4 A= 3 6 -2 - 4 4 5 -6 -4 4 9 (Marks: 6)
appreciate a clear explanation .tks (thumbup)
1 23 -3 6 7 1 1 2-1 2 4 2 24-2 4 8 (a) Determine the vectors that are in the solution space of A (b) What is the rank of A? (c) What is the dimension of the solution space of A? (d) Determine the vectors that are in the column space of A 13 10
1 23 -3 6 7 1 1 2-1 2 4 2 24-2 4 8 (a) Determine...
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.
2.
3.
4.
5.
Given that B = {[1 7 3], [ – 2 –7 – 3), [6 23 10]} is a basis of R' and C = {[1 0 0], [-4 1 -2], [-2 1 - 1]} is another basis for R! find the transition matrix that converts coordinates with respect to base B to coordinates with respect to base C. Preview Find a single matrix for the transformation that is equivalent to doing the following four transformations...
10
a) Find a basis and the dimension of the row space.
b) Find a basis and the dimension of the column space.
c) Find a basis and the dimension of the null space.
d) Verify the Dimension Theorem for A
e) Identify the Domain and Codomain if this is the standard
matrix for a linear transformation
f) What does the row space represent when this is viewed as a
linear transformation?
g) Does this represent a linear operator? Explain....
1. Find a basis for the null space and row space of 1-13 (a) A 5-4 -4 7 -6 2 2 0 3 (b) A544 7 -6 2
1. Find a basis for the null space and row space of 1-13 (a) A 5-4 -4 7 -6 2 2 0 3 (b) A544 7 -6 2
4. A= -2 4 -2 2-6-3 8 2 B= 1 -3 1 0 6 - 7 0 2 5 -5 0 0 0 -4 bases for the column space and null space of A.
(1 point) Find a basis for the column space of 0 A = -1 2 3 3 - 1 2 0 - 1 -4 0 2 Basis = (1 point) Find the dimensions of the following vector spaces. (a) The vector space RS 25x4 (b) The vector space R? (c) The vector space of 6 x 6 matrices with trace 0 (d) The vector space of all diagonal 6 x 6 matrices (e) The vector space P3[x] of polynomials with...
[1 0 O1[i 2 0 3 6. (4) Let A 3 1 0l0 0 3 1. Without multiplying the matrices, 0 -1 1110 0 0 0 (a) Find the dimension of each of the four fundamental subspaces. b have a solution? (b) For what column vector b (b, b2, ba)' does the system AX (c) Find a basis for N(A) and for N(AT).
[1 0 O1[i 2 0 3 6. (4) Let A 3 1 0l0 0 3 1. Without...