sir please A is 64times17 matrix rank11 Ax 0 Show number li

sir please...

A is (64times17) matrix, rank=11. A_x = 0, Show number linearly independent vector x. A^Ty = 0. Show number linearly independent vector y. 34. row space and null space include vector (1,1,1)^T .Show matrix. 35. (x_1,x_2,x_3, ... ,x_117) A = (x_117, x_1, x_2, ... , x_116). Show matrix A determinant. 36. PA = LU [0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0] [0 0 1-3 2 2 -1 4 2 1 4-2 9 1 4 2-1 5-1 5] =[1 0 0 0 0 1 0 0 1 1 1 0 2 1 0 1] [2-1 4 2 1 0 1-3 2 0 0 0 0 2 0 0 0 0 0] (a) What is rank of A? (b) What is a basis for the row space of A? (c) What is a basis for the column space of A? (d) What is the dimension of the left nullspace of A? (e) What is the general solution to Ax = 0?

Solution

Ans(33):

We know that

number of columns in matrix = rank+nullity

case Ax=0

64x17 means number of columns =17

given rank=11

then 17=11+nullity

or nullity=6

Hence there are 6 linearly independent vectors.

--------------------

case A^Ty=0

64x17 is order of A then A^T will be of order 17x64 which means means number of columns =64

given rank=11

then 64=11+nullity

or nullity=53

Hence there are 53 linearly independent vectors.