Ch1 Linear Equations

Question 1

How do we know if a system of Linear Equations has No Solutions ?

Answer 1

If any part of the Matrix has a value of 0 = #

Question 2

How do we know if a system of Linear Equations has Infinite Solutions ?

Answer 2

If any part of the Matrix has a value of 0 = 0

Question 3

How do we know if a system of Linear Equations has a Finite Solution ?

Answer 3

If the RREF shows 1 for each variable.

Question 4

Explain how to obtain the Solution:

Answer 4

Since we checking to see if two vectors can combine to form out vector b, all we have to do is set up arbitrary coefficients x₁ and x₂, multiply them into our two vectors, then solve for B

Question 5

How is Dot Product of a Matrix Performed ? What are the conditions ?

Answer 5

So long as the number of Columns in the 1st Matrix match the number of Rows in the 2nd Matrix, We can multiply Row x Column

Question 6

How do you find the equation of the line which this matrix intersects ?

Answer 6

We start by solving the system of equations to the point where we notice a line forms the intersections.

we can then take away one of the lines in the matrix and solve for two seperate equations with respect to x₃ or x₂