Answer to Question #87345 in Linear Algebra for Daniel

Question

1.Given that x + 2y = 3, 3x + 4y =1. What is x and y?
a.(1,-1)
b.(2,-2)
c.(-5,4)
d.(4,-5)

2.Given that
(1 3)
(k 4)
is singular matrix. Find the value of k
a.(4/3)
b.(3/5)
c.(3/4)
d.(5/3)

Answer 1

1) We have $x = 3x + 4y - 2(x + 2y) = 1 - 6 = -5.$ Then calculate $y = \frac{3 - x}{2} = \frac{8}{2} = 4.$ Answer: c.

2) We have $1 \cdot 4 - 3k = 0.$ Then $k = \frac{4}{3}.$ Answer: a.