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 Pn denote the vector space over the reals of polynomials p(x) of degree n with coefficients in the real numbers. Let the linear map ϕ:P4→P4 be defined by: ϕ(p(x))=p(a)+p(bx+c).Using the standard basis for range and domain find the matrix given by ϕ.
-
Question in Linear Algebra
Let Pn denote the vector space over the reals of polynomials p(x) of degree n with coefficients in the real numbers.
Let the linear map ϕ:P4→P4 be defined by:
ϕ(p(x))=ap(x)+(bx+c)p′(x)+(x2+dx+f)p″
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 "pre-Fourier series" setting.