Note: All the questions in this quiz will be related to the matrix A given below

Question

Note: All the questions in this quiz will be related to the matrix A given below. You should feel free to use results from one question when solving another. In fact, its what I intend for you to do! A = [1 -1 2 -5 -3 2 -2 1 -1 0 0 0 3 -5 2] Is x =[2 1 -4 -2 -1] in the nullspace of A? Is y = [6 -6 -1 4 -2]| in the rowspace of A? Is z = [3 6 9]in the columnspace of A? What is the reduced row echelon form of A? Find a basis for the nullspace of A. Find a subset of the columns of A that form a basis for the columnspace of A. Find a basis for the rowspace of A.

Explanation / Answer

1)

1)

The nullspace of A Find the dimension (= nullity(A)) and a basis. In e?ect, solve

the linear system Ax = 0. Therefore we use elementary row operations to reduce A

to row echelon form (not uniquely, so your answer may vary)

null space means AX = 0

2*1+1*-1+2*-4+5*2+3*1 =6

no it is not in the null space of matrix

it is not getting zero so it is not null space for this matrix

2)

The row space of A Find the dimension (= rank(A)) and a basis.

here rank of the matrix 2

r(A) = 2

row space {1 -1 2 -5 -3}, {2 -2 1 -1 0}

3)

similarly column space

{2 1 3 } ,{-5 -1 -5}

4)

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