sir please... A is (64times17) matrix, rank=11. A_x = 0, Show number linearly in
ID: 3410688 • Letter: S
Question
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?Explanation / Answer
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.
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