16 results authored by John Steele  search across all users.

Question in John's workspace
Using the reduction formulas for products of powers or sin and cosine

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

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

Question in Linear Algebra
Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Question in Linear Algebra
Multiplication of $2 \times 2$ matrices.

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

Question in Linear Algebra
Elementary Exercises in multiplying matrices.

Question in Linear Algebra
Three examples of determinant of 2x2 matrices.

Question in Linear Algebra
Multiplication of two matrices.

Question in Linear Algebra
This question tests students knowledge of basic matrix arithmetic.

Exam (5 questions) in Linear AlgebraA collection of questions on solving equations and revising manipulation of small matrices for 2nd year students

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

Question in John's workspace
Calculation of the length and alternative form of the parameteric representation of a curve.

Question in John's workspace
A question to test integration by parts in a "preFourier series" setting.