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Represent a linear map as a matrix with a given basis
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 $\phi$.
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Last modified 18/02/2019 19:22
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Represent a linear map as a matrix given a basis
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 $\phi$.
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Last modified 18/02/2019 19:14
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Last modified 15/02/2019 19:26
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Solve a separable first order ODE,
Find the solution of a first order separable differential equation of the form $axyy'=b+y^2$.
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Last modified 15/02/2019 19:21
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Question Has some problems
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Last modified 15/02/2019 11:00
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Exam (1 question) Draft
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Last modified 15/02/2019 10:59
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Solve a separable first order ODE,
Find the solution of a first order separable differential equation of the form $(a+x)y'=b+y$.
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Last modified 12/02/2019 17:46
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PDF and CDF of continuous uniform random variable,
$X$ is a continuous uniform random variable defined on $[a,\;b]$. Find the PDF and CDF of $X$ and find $P(X \ge c)$.
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Last modified 08/02/2019 15:20
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Precedence of operators  everything except indices
Questions testing understanding of the precedence of operators using BIDMAS. These questions only test BDMAS. That is, they test Brackets, Division/Multiplication and Addition/Subtraction.
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Last modified 08/02/2019 15:14
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Precedence of operators  everything except brackets
Questions testing understanding of the precedence of operators using BIDMAS applied to integers. These questions only test IDMAS. That is Indices, Division/Multiplication and Addition/Subtraction.
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Last modified 08/02/2019 15:11
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