1. + -14 points HoltLinAlg2 4.3.001 Consider the following matrices. (To make yo

Question

1. + -14 points HoltLinAlg2 4.3.001 Consider the following matrices. (To make your job easier, an equivalent echelon form is given for the matrix.) 1-3 21 10-10 3 8-2 Find a basis for the column space of A. (If a basis does not exist, enter DNE into any cell.) Find a basis for the row space of A. (If a basis does not exist, enter DNE into any cell.) Find a basis for the null space of A. (If a basis does not exist, enter DNE into any cell.) Verify that the Rank-Nullity Theorem holds. (Let m be the number of columns in matrix A.) rank(A) nullity(A) = rank(A) + nullity(A) = =m

Explanation / Answer

a basis for column space of A is

[1] [-3]

[-2] [5]

[-3] [8]

a basis for Row space of A is

[ 1 -3 2]

[-2 5 0]

Basis for the null space of A is

x-10z=0

y-4z=0

i.e. x= 10z

and y= 4z

so [x] = [ 10z]

[y] [4z]

[z] [z]

so the basis for null space is

(10, 4 ,1)

Rank(A) is m-1

nullity(A)= 1

Rank(A)+nullity(A)= m-1+1

=m

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