Linear Algebra for Machine Learning and Data Science (8)

Solving systems of linear equations

Check your knowledge

Q1

Solve the system of equations below (Videos: Solving non-singular system of linear equations)

$$ \begin{cases} 4x + 3y = 6 \\ x - 5y = 8 \end{cases} $$

y = -26/23

x = 54/23

Q2

Solve the system of equations below: (Videos: Solving singular system of linear equations, Solving systems of equations with more variables)

$$ \begin{cases} 4x + 3y + z = 6 \\ x - 5y + 7z = 8 \\ 5x - 2y + 8z = 14 \end{cases} $$

The system has infinitely many solutions since the second equation is the third one minus the first one

Q3

Is the matrix above in row echelon form? If not, compute the row echelon form of the matrix. (Videos: Row echelon form, Row echelon form in general, Reduced row echelon form)

No

x + 3/4y + 1/4z = 3/2

0x + y - 27/23z = -26/23

0x + 0y + 0z = 0

Q4

What is the rank of M? (Videos: The rank of a matrix, The rank of a matrix in general)

2

Q5

What are the operations that can be done in a row of a matrix that preserves its singularity? (Videos: Matrix row-reduction, Row operations that preserve singularity)

Switching rows

Multiplying a row by a scalar

Adding a row to another one

All the information here is based on the Linear Algebra for Machine Learning and Data Science | Coursera from DeepLearning.AI