Question 4 12 pts 1 -1 1 1 0 1 -1 (a) Consider the matrix )...

Question

Question

Question 4 12 pts 1 -1 1 1 0 1 -1 (a) Consider the matrix ) = 1 0 1 3 1 -3 (i) Find the space B of all vectors b € R3 such th

math algebra

Answer 1

Similar Homework Help Questions

4. Consider the matrix [1 0 01 A- 1 0 2-1and the vector b2 (a) Construct...

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...
1. Consider the matrix 12 3 4 A 2 3 4 5 3 4 5 6...

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)?
Question 3) (8 points) Consider the following matrix: A= ſi 4 0 0 28 3 12...

Question 3) (8 points) Consider the following matrix: A= ſi 4 0 0 28 3 12 2 11 -5 5 6 0 8 1 (a) Find a basis for the Rowspace(A). Then state the dimension of the Rowspace(A). (b) Find a basis for the Colspace(A). Then state the dimension of the Colspace(A). (e) Find a basis for the Nullspace(A). Then state the dimension of the Nullspace(A). (d) State and confirm the Rank-Nullity Theorem for this matrix.

eclass.srv.ualberta.ca 2 of 2 1. Consider the matrix 3-2 1 4-1 2 3 5 7 8...

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.)...
7. Consider the following matrices 2 3-1 0 1 A=101-2 3 0 0 0-1 2 4...

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...
Consider the matrix 0 4 8 24 0-3-6 3 18 A-0 24 2 -12 0 -2-3...

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...

1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4...

1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a +36) (which is a subspace of Re"). 2. (12 pts) Given the matrix in a R R-E form: -21 1 [1 0 0 0 3 0 1 1 0 - 2 0 0 0 1 0...
1 (8+7 15 pts) Linear equations Consider the system of equations 1 -1 0 0 0...

1 (8+7 15 pts) Linear equations Consider the system of equations 1 -1 0 0 0 0 1 2-1 03 - 0 0 1 2 3 4 4 (a) Determine all values of a and b such that this system is 1 inconsistent (ii) consistent (b) Find the set of solutions for 1 a b 2.
1 — 0 1 1 [R |d 1 Consider the augmented matrix [A | b) and...

1 — 0 1 1 [R |d 1 Consider the augmented matrix [A | b) and its reduced row echelon form [Ra]: 2 -2 0 23 6 0 4 0 7 / 4 -1 -1 0-15 | -5 row operations -3 0 [ A ] b] = 81 -2 -4 4 -35-10 0 0 0 11 12 3 6 -60 69 18 0 0 0 0 0 1 0 (a) Write the vector form of the general solution to the...

For the following questions, consider the matrix: ſi 0 21 0 1 0 A= 1 -1...

For the following questions, consider the matrix: ſi 0 21 0 1 0 A= 1 -1 2 0 1 0 1 Please circle the correct answer in parts (a.)-(e.). (a.) The rank of A is 1 2 3 4 (b.) Any basis for the range space of A, R(A), will consist of how many vectors? 1 2 3 4 (c.) The dimension of the null space of A, dim(N(A)) is: 0 1 2 3 (d.) The following vector is in...