**Question 1: **

Given the two vectors v_{1} = (2, 3) and v_{2} = (-2,-3), find the following graphically and write the result:

V_{1} - v_{2}, v_{1}v_{2}, x v_{1}, x v_{2}

**Question 2:**

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

2x + y = 3

3x =4

**Question 3:**

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

2x + 3y = 5

-x + 2y = 2

y = 2 + 0.5x

**Question 4:**

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

**Question 5:**

A dynamic system is defined by the following set of equations:

x^{.}1(t) = Ax (t) + bu(t)

y^{.}(1) = cx (t-1)

Where X(t) = [x_{1} x_{2}]^{T} ∈ R^{2} is the system state vector, u(t) ∈ R is the system input vector, y(t) ∈ R is the system output vector, x^{.}(t) = dx(t)/dt ≅ x(t_{2}) - x(t_{1})/(t_{2} - t_{1}) is the first derivative of state vector, A ∈ R^{2x2}, and c ∈ R^{1x2} are the system parameters matrices.

An experiment was done to collect data and the obtained data is

t | u | x1 | x2 | y |

0 | 0 | 2 | -1 | 1.5 |

1 | 1 | 1.8097 | -0.6042 | 1.5076 |

2 | 1 | 2.5891 | 1.2183 | 3.1983 |

3 | 1 | 3.2944 | 2.3194 | 4.4541 |

4 | 1 | 3.9325 | 2.9846 | 5.4249 |

5 | 1 | 4.51 | 3.3866 | 6.2032 |

6 | 1 | 5.0324 | 3.6294 | 6.8471 |

7 | 1 | 5.5052 | 3.7761 | 7.3932 |

8 | 1 | 5.9329 | 3.8647 | 7.8653 |

9 | 1 | 6.32 | 3.9183 | 8.2791 |

10 | 1 | 6.6702 | 3.9506 | 8.6455 |

Calculate the system parameter matrices A ∈ R

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