The document addresses the ranks of two matrices, a and b. For matrix a, both the first and second rows are linearly independent, resulting in a rank of 2. For matrix b, while the first and second rows are independent, the third and fourth rows are linear combinations of the first two, also resulting in a rank of 2.

1. 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