Matrix and Vectors? ?

Question

A = 2 1.............b = 3

......4 3...................4

Given the matrix A and vector b and an unknown vector x

such that x = x1

....................x2

expand as a set of equations and solve them to find x

Extra info:

The x1 and x2 actually have x with a small number to the bottom right corner of the x, like a power but bottom right not top right. The dots are just for spacing. I hope its understandable.

Answer 1

Starting witt the matrix-vector equation

Ax = b

You can get a system of equations by multiplying A into b. The system is

2x1 + x2 = 3

4x1 + 3x2 = 4

To solve, multiply the first equation by -2 and then add them together to eliminate x1.

-4x1 - 2x2 = -6

4x1 + 3x2 = 4

----------------------

x2 = -2

Using the first equation

2x1 + x2 = 3

2x1 -2 = 3

x1 = 5/2

So the solution is the vector

[x1] -- [5/2]

[x2] -- [-2 ]