CraigsMaths

Mathematics Teaching for Learning

Archive for August, 2008

Adding and subtracting matrices

Friday, August 8th, 2008

Matrix addition and subtraction is fairly simple. Just remember that we can only add or subtract matrices if they have the same dimensions. The number of rows must be equal in each matrix and the number of columns must be equal in each matrix.

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What are matrices?

Friday, August 8th, 2008

Matrices are simply arrays of values. We use them as a tool to ease operations such as solving simultaneous equations, working with vectors and transformations.

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Finding determinants of a 3×3 matrix

Friday, August 8th, 2008

It is fairly simple to memorise the formula for the determinant of a 2×2 matrix:

\mathit{A}=\begin{bmatrix}<br />
a & b \\<br />
c & d<br />
\end{bmatrix}

\left|\mathit{A} \right|=ad-cb

Here we look at a simple approach that aids memorising the formula for a 3×3 matrix called Sarrus’ rule which will give you the determinant of a 3×3 matrix.

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Quadratic general to standard form

Wednesday, August 6th, 2008

When solving quadratic equations and sketching parabolas you can get the required points onto your graph very quickly if you know how to convert from the general form of y=ax^{2}+bx+c to the standard form of y=a\left(x-h\right)^{2}+k. (See Standard Quadratic Form for the reasons why.) This article explains how to complete the square to acheive this.

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Parabolas

Tuesday, August 5th, 2008

A parabola is a curve that is described by a quadratic equation. You may be presented with a quadratic equation in one of several forms and then asked to:

  • Sketch a graph of the equation
  • Find the local maxima or local minima
  • Find the vertex coordinates
  • Find the x-intercept(s) if they exist
  • Find the the y-intercept
  • Find the axis of symmetry

This article will describe the simplest approach for the different forms of the quadratic equation.

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