Check whether the following set of vectors are linearly dependent or independent.
(a) S = {(1, 2, −2, −1),(2, 1, −1, 4),(−3, 0, 3, −2)}
(b) S = {(1, 3, −2, 5, 4),(1, 4, 1, 3, 5),(1, 4, 2, 4, 3),(2, 7, −3, 6, 13)}

 Whether the system below is consistent? Justify.
x + 2y − 3z = 1
3x − y + 2z = 5
5x + 3y − 4z = 2

Solve
x + 2y − 3z + 2w = 2
2x + 5y − 8z + 6w = 5
3x + 4y − 5z + 2w = 4

For the system
x + 2y − z = 0
2x + 5y + 2z = 0
x + 4y + 7z = 0
x + 3y + 3z = 0 

Find the solution space as well as dimension.

The square root of 0.0081 is ………

What is the sum of 5x3 – 3x2 - 1 and 3x2 + 1?

All natural numbers and 0 are called the ……………….. numbers?

The wages of 10 workers for a six-day week is $ 1200. What are the one day’s wages of 4 workers?

The average of first 50 natural numbers is ……

A fraction which bears the same ratio to 1/27 as 3/11 bear to 5/9 is equal to ………..??

A clock strikes once at 1 o’clock, twice at 2 o’clock, thrice at 3 o’clock and so on. How many times will it strike in 24 hours?