Topics Covered

System of Linear Equation

• Form and graphically interpret 2x2 and 3x3 systems of linear equations
• Determine the number of solutions to a 2x2 and 3x3 system of linear equations
• Distinguish between singular and non-singular systems of equations
• Determine the singularity of 2x2 and 3x3 system of equations by calculating the determinant

Solving System Of Linear Equations

• Solve a system of linear equations using the elimination method.
• Use a matrix to represent a system of linear equations and solve it using matrix row reduction.
• Solve a system of linear equations by calculating the matrix in the row echelon form.
• Calculate the rank of a system of linear equations and use the rank to determine the number of solutions of the system.

Vectors and Linear Transformation

• Perform common operations on vectors like sum, difference, and dot product.
• Multiply matrices and vectors.
• Represent a system of linear equations as a linear transformation on a vector.
• Calculate the inverse of a matrix, if it exists.

Determinants and EigenVectors

• Interpret the determinant of a matrix as an area and calculate determinant of an inverse of a matrix and a product of matrices.
• Determine the bases and span of vectors.
• Find eigenbases for a special type of linear transformations commonly used in machine learning.
• Calculate the eignenvalues and eigenvectors of a linear transformation (matrix).