Given a 3x3 matrix with very big elements, perform row operations to find a matrix with single-digit elements. Then reduce that to an upper triangular matrix, and hence find the determinant.

Given a 3x3 matrix with very big elements, perform row operations to find a matrix with single-digit elements. Then reduce that to an upper triangular matrix, and hence find the determinant.

Very elementary matrix multiplication. 

Questions on matrix arithmetic.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

Given a matrix in row reduced form use this to find bases for the null, column and row spaces of the matrix.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: \[\phi(p(x))=p(a)+p(bx+c).\]Using the standard basis for range and domain find the matrix given by $\phi$.

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers.

Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:

$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$

Using the standard basis for range and domain find the matrix given by $\phi$.

Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

Cofactors Determinant and inverse of a 3x3 matrix.

Multiplication of  matrices of different sizes.

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Cofactors Determinant and inverse of a 3x3 matrix.

Find the determinant of a $3 \times 3$ matrix.

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Multiplication of $2 \times 2$ matrices.

Cofactors Determinant and inverse of a 3x3 matrix.

Multiplication of $2 \times 2$ matrices.

Elementary Exercises in multiplying matrices. 

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Find the determinant of a $3 \times 3$ matrix.

This question tests learner's knowledge of the inverse matrix method for a 3x3 matrix.

Elementary Exercises in multiplying matrices. 

Find the determinant of a $3 \times 3$ matrix.

Cofactors Determinant and inverse of a 3x3 matrix.

Multiplication of $2 \times 2$ matrices.

This question tests students knowledge of basic matrix arithmetic.

Multiplication of $2 \times 2$ matrices.