Question

if A is 3*5 matrix such that A has 3 pivot entries then the dimension of null A is​

Answer 1

Answer:

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Answer 2

Answer:

The dimension of null A is 2

Step-by-step explanation:

A is a 3 × 5 matrix and it has 3 pivot entries

The matrix A has 3 rows and 5 columns

$Col(A)=R^{3}$

Matrix A has 5 columns and 3 pivot columns

So, col(A) is a three-dimensional subspace of $R^{3}$

The dimension of the column space of A is rank A. So, rank (A) = 3

By using the rank nullity theorem

n = nul(A) + rank(A)

Here n = number of columns of A

n = nul(A) + rank(A)

5 = nul(A) + 3

nul(A) = 5 - 3

nul(A) = 2

Therefore the dimension of null A is 2