Matrices, Determinants and Systems of Linear Equations
Matrices and Determinants
Matrix definition
Square matrices
The identity matrix
Vectors
The transpose of a matrix
Basic matrix operations
Matrix addition and subtraction
Scalar multiplication of a matrix
Matrix multiplication
The matrix-vector product
The determinant of a matrix
Expanding a determinant by cofactors
Calculating the value of a determinant
The determinant of a 2-by-2 matrix
The determinant of a 3-by-3 matrix
Properties of determinants
The inverse of a matrix
Systems of Linear Equations
Solving systems of equations using matrices
Inverse matrix method
Cramer’s rule
Cramer’s Rule and
inverse matrix method correlation
Cramer’s rule (using the determinant) to solve systems of linear equations
Solving system of two equations in two unknowns using Cramer's rule
Solving system of three equations in three unknowns using Cramer's rule
Method of expanding a determinant of a rank n by cofactors
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