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Emma W.

Year 13, Auckland Grammar School

Liam T.

Year 12, Christchurch Boys' High

Sophia C.

Year 13, Wellington Girls' College

Oliver K.

Year 12, Hamilton Boys' High School

Isla M.

Year 13, Rangitoto College, Auckland

Noah P.

Year 12, Burnside High School

Ava S.

Year 13, Westlake Girls High School

Jack R.

Year 12, Nelson College

Charlotte B.

Year 13, Epsom Girls Grammar School

Thomas H.

Year 12, Palmerston North Boys' High

Grace L.

Year 13, Waikato Diocesan School

William T.

Year 12, Kings College, Auckland

Dr. Olivia M.

Mathematics Department, University of Auckland

Prof. James W.

Mathematics Faculty, Victoria University of Wellington

Sarah K.

TA, Mathematics Department, University of Canterbury

Linear Algebra Topics

Linear Equations with Matrices

Notation of matrices

Solving systems of linear equations by graphing

Representing linear system as a matrix

The three types of matrix row operations

Solving a linear system with matrices using Gaussian elimination

Row reduction and echelon forms

Linear combination and vector equations in \(R^n\)

Matrix equation Ax=b

Solution sets of linear systems

Application of linear systems

Linear Transformation

Linear independence

Image and range of linear transformations

Properties of linear transformation

The matrix of a linear transformation

Matrix Operations

Adding and subtracting matrices

Multiplying a matrix by a scalar

Multiplying a matrix by another matrix

Zero matrix

Identity matrix

Properties of matrix addition

Properties of matrix scalar multiplication

Properties of matrix to matrix multiplication

Determinant of a Matrix

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

Properties of determinants

Solving linear systems using Cramer's Rule

Inverse of Matrices

2 x 2 invertible matrix

The inverse of a 2 x 2 matrix

Solving linear systems using 2 x 2 inverse matrices

The inverse of a 3 x 3 matrices with matrix row operations

The invertible matrix theorem

Subspace of \(\Bbb{R}^n\)

Properties of subspace

Column space

Null space

Dimension and rank

Eigenvalue and Eigenvectors

Eigenvalues and eigenvectors

The characteristic equation

Diagonalization

Complex eigenvalues

Discrete dynamical systems

Orthogonality and Least Squares

Inner product, length, and orthogonality

Orthogonal sets

Orthogonal projections

Least-squares problem

Applications to linear models

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Get Instant Linear Algebra Help: Practice Tests + Video Solutions

Most students boost their NCEA results within weeks. Start your free practice test now and join thousands of Kiwi students improving their Linear Algebra skills with StudyPug!

📈

95% of students improve their NCEA results within 30 days

🎯

Average grade improvement of 15% in Linear Algebra

🏆

Over 10,000 practice problems completed daily by NZ students

⏱️

Students save an average of 5 hours per week on homework

Clear Linear Algebra Help

Better NCEA Results

Linear Algebra Practice

Linear Algebra Topics

Linear Equations with Matrices

Linear Transformation

Matrix Operations

Determinant of a Matrix

Inverse of Matrices

Subspace of \(\Bbb{R}^n\)

Eigenvalue and Eigenvectors

Orthogonality and Least Squares

Try Us for Free and Start Doing Better Today

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