Let A 2 3 4 - 1-6 -20 3 6 -9 5 3 -2 7 Find each of the following bases. Be sure to show work as needed. 1 Find a basis for the null space of A. b. Find a basis for the column space of A. c. Find a basis for the row space of A. d. Is [3 2 -4 3) in the row space of A? Explain your reasoning.
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?
Consider the matrix 0 4 8 24 0-3-6 3 18 A-0 24 2 -12 0 -2-3 0 7 0 3 5 [51 [51 a) Find a basis for the row space Row(A) of A (b) Find a basis for the column space Col(A) of A (c) Find a basis space d) Find the rank Rank(A) and the nullity of A (e) Determine if the vector v (1,4,-2,5,2) belongs to the null space of A. - As always,[5 is for the...
Problem 2 A matrix A is given by 2 3 0 1 7 2 1 13 16 3 -5 -3 8 22 -1 -1 -11 -18 Find a basis for N(A) (the null space of A). Find a basis for RaneA) = C(A) (the range, or column space of A) Problem 2 A matrix A is given by 2 3 0 1 7 2 1 13 16 3 -5 -3 8 22 -1 -1 -11 -18 Find a basis for...
11 1 4 15 2. let A lo 1 -9 1 3 7 (a) Explain how would you find a basis for the column space of A. (b) Use the Gram-Schmidt process to produce an orthogonal basis for Col A.
5. Let 5 6 7 8 9 10 11 12 Give a basis for its row space S and a basis for its column space Se
[1 2 0 1] 10. Let A 2 3 1 1 13 5 1 2 (a). Find the reduced row echelon form of A. (b). Using the answer for (a), find rank(A), and find a basis for Col(A). 11. Let A= Find a matrix P such that P-1AP is a diagonal matrix,
Problem 1 Let A= 3 2 13 1 5 7 11 8 -3 9 10 -6 -4 12 8 a) [4 pts) Find a basis for N(A) in rational format. b) (3 pts) Find a particular solution to the matrix equation A*x= 5 -2 14 c) [3 pts] Use your answers in a), b) and the Superposition Principle to express the general solution in vector form to the matrix equation in b).
The matrix A=[-17-51-85-21 is row equivalent to R=「1 3 5 15 45 75 1 -4 -12 -20 0 1. a. Find a basis for the row space of A, row(A) b. Write the sum of the 1st and 3rd row of A as a linear combination of your basis for row(A). 2. a. Find a basis for the column space of A, col(A) b. Write the difference if the 2nd and 4th column of A as a linear combination of...
a brief explanation of each Question 2 | 13 points Show details of your work. [1 -2 0 0 3 [1 0 0 -2 37 2 -5 -3 -2 6 0 1 0 -1 0 Given matrices 0 5 15 100 and 00110 (2 6 18 8 6 0 0 0 0 0 where the matrix R is the reduced echelon form of the matrix A. a) [2 points Find a basis of the Row(A) {{1,0,0,–2,3], [0,1,0, -1,0], [0,0,1,1,0}} b)...