Linear Algebra Answers

If the numerator of a fraction is doubled and the denominator is increased by 7, the value becomes 2/3; but if the denominator is doubled and the numerator is increased by 2, the value becomes 3/5. What is the original fraction?

A and B are running on a track having 8 laps to mile. If they run in opposite directions, they meet every 20 seconds. If they run in the same direction, it requires 3 minutes for A to overtake B. Find the rate of each in feet per second.

How much copper and how much magnesium should be added to 200lbs of an alloy containing 20% copper and 40% magnesium to produce an alloy containing 24% copper and 50% magnesium?

The sum of the digits of a three-digit number is 11. If the first and last digits are interchanged, the new number is greater than the original number by 594. If the tens and the units digits are interchanged, the resulting number is greater than the original by 36. Find the original number.

A man wishes to fence in a rectangular lot. If he uses material costing P17/meter for the front of the lot and material costing P14/meter for the other three sides, the fence will cost P8,900. If he uses the cheaper material for all four sides, the fence will cost P8,540. Find the dimensions of the lot.

A man rows 12 miles downstream on a river in 2 hrs. He requires another 3 hrs. to row back to his starting position. Find the speed of the current and the rate the man can row in still water.

Two pipes empty a vat in 1hr and 12 min. When one pipe is used to fill and one to empty the vat, it is filled in 3 hrs. How long would it take each pipe to empty the vat if only one pipe is open?

Determine whether W = {(x, y,z) | x + y + z + 1 = 0, x, y,z ∈ R} a subspace of R³ or

not?

Which of the following linear systems is homogeneous. I) 3x + 14y = 0 & 2x − 3y = 7 II) 7x + 2y = 10 & 11x − 0y = 7 III) 4x − 23y = 0 & 7x − 3y = 0

Prove that if U and V are subspaces of Rn

so is U+V