16 results authored by John Steele - search across all users.

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• Question

Using the reduction formulas for products of powers or sin and cosine

• Question

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 $\phi$.

• Question

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 $\phi$.

• Question

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

• Question

Reduce a 5x6 matrix to row reduced form and using this find rank and nullity.

• Question

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

• Question

Multiplication of $2 \times 2$ matrices.

• Question

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

• Question

Elementary Exercises in multiplying matrices.

• Question

Three examples of determinant of 2x2 matrices.

• Question

Multiplication of two matrices.

• Question

This question tests students knowledge of basic matrix arithmetic.

• Exam (5 questions)
A collection of questions on solving equations and revising manipulation of small matrices for 2nd year students
• Question

Given $6$ vectors in $\mathbb{R^4}$ and given that they span $\mathbb{R^4}$ find a  basis.

• Question

Calculation of the length and alternative form of the parameteric representation of a curve.

• Fourier series primer