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Exponents & Logarithms Rounding & Error Sequences & Series Financial Mathematics Matrices Complex Numbers

Calculator Skills

Review Videos Formula Booklet

Dashboard

Topics

Exponents & Logarithms Rounding & Error Sequences & Series Financial Mathematics Matrices Complex Numbers

Calculator Skills

Review Videos Formula Booklet

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Matrix addition and multiplication, determinants and inverses M−1=detM1(a−c−cd),

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Foundations of Matrices

Matrix notation and order m×n, together with addition and subtraction of matrices of the same order, scalar multiplication, matrix multiplication and its required dimensions, the zero matrix, and the properties of multiplication including non-commutativity, associativity and distributivity, with calculator use for numeric matrices.

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Identity, Inverses & Determinants

Identity matrices , inverses and determinants of square matrices, including IM=MI=M, the inverse condition detM=0⟺M−1 exists, finding 2×2 determinants and inverses by hand, using technology for larger matrices, and rearranging matrix equations such as AB=C to solve for unknown matrices.

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Geometric Transformations with Matrices

Matrix representations of geometric transformations in the plane, including images of basis vectors under a 2x2 matrix, enlargements and horizontal or vertical stretches, rotations, reflections, translations, composition of transformations using matrix products, and area scale factor ∣detM∣.

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Systems of equations with Matrices

Writing systems of linear equations in matrix form Ax=b, solving them using x=A−1b when A−1 exists, and interpreting detA=0 as giving no solution or infinitely many solutions.

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Eigenvalues & Eigenvectors

Eigenvalues and eigenvectors defined by Av=λv, finding eigenvalues from det(A−λI)=0 and the characteristic polynomial, finding eigenvectors by solving the resulting simultaneous equations, and diagonalizing matrices as A=PDP−1 for distinct real eigenvalues, including using diagonal form to exponentiate matrices.

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Home

Matrix addition and multiplication, determinants and inverses M−1=detM1(a−c−cd),

Progress trend

2 weeks

All time

0%overall progress

Sign up to view your learning progress

Learning path

Follow the recommended order, or open any concept.

Start Here

Foundations of Matrices

Matrix notation and order m×n, together with addition and subtraction of matrices of the same order, scalar multiplication, matrix multiplication and its required dimensions, the zero matrix, and the properties of multiplication including non-commutativity, associativity and distributivity, with calculator use for numeric matrices.

0/0 key exercises

Thumbnail for Foundations of Matrices

Identity, Inverses & Determinants

Identity matrices , inverses and determinants of square matrices, including IM=MI=M, the inverse condition detM=0⟺M−1 exists, finding 2×2 determinants and inverses by hand, using technology for larger matrices, and rearranging matrix equations such as AB=C to solve for unknown matrices.

0/0 key exercises

Thumbnail for Identity, Inverses & Determinants

Geometric Transformations with Matrices

Matrix representations of geometric transformations in the plane, including images of basis vectors under a 2x2 matrix, enlargements and horizontal or vertical stretches, rotations, reflections, translations, composition of transformations using matrix products, and area scale factor ∣detM∣.

0/0 key exercises

Thumbnail for Geometric Transformations with Matrices

Systems of equations with Matrices

Writing systems of linear equations in matrix form Ax=b, solving them using x=A−1b when A−1 exists, and interpreting detA=0 as giving no solution or infinitely many solutions.

0/0 key exercises

Thumbnail for Systems of equations with Matrices

Eigenvalues & Eigenvectors

Eigenvalues and eigenvectors defined by Av=λv, finding eigenvalues from det(A−λI)=0 and the characteristic polynomial, finding eigenvectors by solving the resulting simultaneous equations, and diagonalizing matrices as A=PDP−1 for distinct real eigenvalues, including using diagonal form to exponentiate matrices.

0/0 key exercises

Thumbnail for Eigenvalues & Eigenvectors

Matrices

solving systems of equations with inverses, and diagonalization using eigenvectors.

Also geometric transformations with matrices (Topic 3)

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Practice by difficulty level.

IB: 5

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9 problems

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Matrices

solving systems of equations with inverses, and diagonalization using eigenvectors.

Also geometric transformations with matrices (Topic 3)

Problem bank

Practice by difficulty level.

IB: 5

Sign up for free to unlock

16 problems

IB: 6

Upgrade to unlock

20 problems

IB: 7

Upgrade to unlock

9 problems

Browse untimed question bank

Performance metrics

Concept Score

0%

+0% today

Speed Score

0%

+0% today

Mastery Score

0%

+0% today

Estimated range: 0%-29%

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Problem activity

No completed problem attempts yet.

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