Solve the given system using a - column-space and output

Question

Problem 1:

Find the following graphically:

1. c₁ + c₂

2. c₁c₂ (inner product)

3.

4.

Problem 2:

Solve the following system using A - column-space and output space:

2x₁ = 3
-x₂ = 4

Problem 3:

Solve the following system using A-row-space and input space:

2x₁ = 3x₂ - 5
2x₂ = 2 - 4x₁

Problem 4:

A linear transformation is applied to the object on the left and we got the object on the right. Find the applied linear transformation matrix.

Problem 5:

Consider the following system of equations:

1. Find the unknown elements using the following information:

P	x	y	X	Y
1	0	10	1	2
2	10	0	30	10
3	10	10	30	20
4	5	5	5	5

2. Using the values form previous question, calculate (x , y) of ( X , Y, Z ) = (2, 2, 2).