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...
eclass.srv.ualberta.ca 2 of 2 1. Consider the matrix 3-2 1 4-1 2 3 5 7 8 (a) Find a basis B for the null space of A. Hint: you need to verify that the vectors you propose 20 actually form a basis for the null space. (Recall: (1) the null space of A consists of all x e R with Ax = 0, and (2) the matrix equation Ax = 0 is equivalent to a certain system of linear equations.)...
1. Consider the following matrix and its reduced row echelon form [1 0 3 3 5 187 [1 0 3 3 0 37 1 1 5 4 1 10 0 1 2 1 0 - A=1 4 1 0 3 3 -1 0 rref(A) = 10 0 0 0 1 3 2 0 6 6 -1 3 | 0 0 0 0 0 0 (a) Find a basis of row(A), the row space of A. (b) What is the dimension...
Please be as detailed as possible. Find a basis for the row space and the rank of the matrix. r-2-8 8 5 З 12-12-4 -2 -8 89 (a) a basis for the row space [1,4,-4,0;0,0,0,1 (b) the rank of the matrix No Response)2 Find a basis for the row space and the rank of the matrix. r-2-8 8 5 З 12-12-4 -2 -8 89 (a) a basis for the row space [1,4,-4,0;0,0,0,1 (b) the rank of the matrix No Response)2
1. Consider the matrix 12 3 4 A 2 3 4 5 3 4 5 6 As a linear transformation, A maps R' to R3. Find a basis for Null(A), the null space of A, and find a basis for Col(A), the column space of A. Describe these spaces geometrically. 2. For A in problem 1, what is Rank(A)?
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...
4. Consider the matrix [1 0 01 A- 1 0 2-1and the vector b2 (a) Construct the augmented matrix [Alb] and use elementary row operations to trans- form it to reduced row echelon form. (b) Find a basis for the column space of A. (c) Express the vectors v4 and vs, which are column vectors of column 4 and 5 of A, as linear combinations of the vectors in the basis found in (b) (d) Find a basis for the...
[15 marks] b) Consider the following matrix: IT 2 0 -17 A = |2 6 -3 -38 3 10 -6 -5| i) Find the rank of A ii) Find a basis for the null-space of A iii) Find a basis for the row space of A [10 marks]
(1 point) Find a basis for the column space, row space and null space of the matrix 8 -4 4 -2 6 2 -5 -4 1 -1 -3 2 -1 Basis of column space: {T Basis of row space: OTT {{ Basis of row space: Basis of null space:
14 points LarApCalc10 3.1.048 12. Consider the following. y--+4, +2x x0 Find the critical numbers. (Hint: Check for discontinuities.) (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation If an answer does not exist, enter DNE.) increasing decreasing Sketch the graph of the function to verify your results. 5 -3 -2 -1 -6-5-43-2-11 1 23 Type...