Linear algebra a What is the rank of A b What is the rank of

Linear algebra:

a) What is the rank of A?

b) What is the rank of B?

Solution

a)

first and second rows are not multiples of each other hence they are linearly independent

Henc, rank(A)=2

b)

First and second rows are linearly independent as first and second rows of A are linearly independent

But third row is 3 times the first row and 4th row is 3 times the second row

So there are only two linearly independent rows

Hence, rank of B=2