Asking the student to create examples of two matrices which multiply to zero but are not themselves the zero matrix. Then getting the student to think about some features of these examples.

Simple exercise in collecting terms in different powers of \(x\)

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

No description given

No description given

No description given

No description given

No description given

No description given

No description given

No description given

No description given

Matrix by scalar and matrix by matrix multiplication exercises.

Exercises in solving simultaneous equations with 2 variables.

Exercises on inverting 2x2 and 3x3 matrices.

Set of matrices exercises for knowledge validation. Topics covered:

• Matrix Addition and Subtraction

Semi-worked example of inverting a 3x3 matrix using cofactor, adjoint and determinant.

Addition and Subtraction by hand questions, whole numbers and decimals. Fully worked solutions in feedback.

Subtraction questions, whole and decimal, to be carried out by hand. Full worked solutions given in feedback.

Addition calculations to be carried out by hand, full worked solutions in feedback.

Semi-worked example of solving simultaneous equations using matrices. Equation values are randomly generated. The student is walked through the steps needed to solve the equations.

No description given

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land$.

For example $\neg q \to \neg p$.

Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.

No description given

No description given

Solve for an angle which will result in equilibrium for a triangle subjected to three couples.   A trial and error solution is recommended.

No description given