Question

0 -3 -6 4 9 [10 2 0 -1] -1 -2 -1 3 1 0 1 -1 0 -2 12. Given A and B = -2 -3 0 3 -1 0 0 0 1 4 5 -9 0 0 0 0 0 (a) (4 points) Find a basis for the column space of A. ܗ ܬ ܚ ܝ with A row equivalent to B. (b) (4 points) Find a basis for the nullspace of A. (c) (2 points) nullity (A)=

Answer 1

Answer: Given. 0 -3 А 4 - 2 3 - - 3 3 4 5 -9 7 1 o 2 o and B. -) 1 0-2 and то O о 1 4 0 o 0 Also. A is now equivalent to (a) We know elementary now operations do affect the column space. However, we make of now reduction to find basis for the column space. Process is following- can still use As A is now equivalent to the matrix B then the columns of A that corresponds to the pivot columns of forom a basis of the column space of A. B 1, 2,4 are pivot columns, Hence, columns of B A basis for the so, column space of A is - 2 -3 . 3 Elementary now operations affect the null space. does not Hence, null space of A= null space of B Nowo null space of XER XER : BY = 0 }

we can also that Therefore a form basis for null they will say space of A. Hence. basis for the null space of A is 2 1 2 1 (C) Nulity (A) Dimension of the null space of A 2