Further Maths - Matricies
See also:
- Further Maths - DeterminantsA
- Further Maths - Inverting MatriciesA
- Further Maths - Solving Systems of Equations Using MatriciesA
- Further Maths - Linear TransformationsA
If a matrix is $m \times n$, how many columns does it have?
$m$ columns.
What are the dimensions of a matrix?
What are the dimensions of
\[\begin{matrix} 3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \end{matrix}\]??
\[3 \times 3\]What are the dimensions of
\[\begin{matrix} 3 & 3 & 3 \\ 3 & 3 & 3 \end{matrix}\]??
\[2 \times 3\]What are the dimensions of
\[\begin{matrix} 3 & 3 \\ 3 & 3 \\ 3 & 3 \end{matrix}\]??
\[3 \times 2\]Visualise a
\[5 \times 2\]matrix??
\[\begin{matrix} 5 & 5 \\ 5 & 5 \\ 5 & 5 \\ 5 & 5 \\ 5 & 5 \end{matrix}\]What are the dimensions of \(\begin{matrix} 3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \end{matrix}\)?
What are the dimensions of \(\begin{matrix} 3 & 3 & 3 \\ 3 & 3 & 3 \end{matrix}\)?
What are the dimensions of \(\begin{matrix} 3 & 3 \\ 3 & 3 \\ 3 & 3 \end{matrix}\)?
Visualise a \(5 \times 2\) matrix?
When can you multiply matrices?
The columns of the first matrix equals the rows of the second matrix.
If two matrices are $m _ 1 \times n _ 1$ and $m _ 2 \times n _ 2$, how can you tell whether you can multiply them?
If two matrices are $m _ 1 \times n _ 1$ and $m _ 2 \times n _ 2$, what will be the size of the resulting multiplied matrix?
What’s the co-ordinate matrix for
\[A(2,1), B(2,7), C(5,1)\]??
\[\begin{matrix} 2 & 2 & 5 \\ 1 & 7 & 1 \end{matrix}\]What are the co-ordinates
\[A, B\]and
\[C\]for
\[\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{matrix}\]??
\[A(1,4) \\ B(2,5) \\ C(3,6)\]What will be the size of the multiplied matrix if you multiply $3 \times 4$ and $4 \times 9$?
What’s a one sentence explanation for matrix multiplication?
You multiply all the rows of the first matrix by the columns of the second matrix.
What’s the co-ordinate matrix for \(A(2,1), B(2,7), C(5,1)\)?
What are the co-ordinates \(A, B\) and \(C\) for \(\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{matrix}\)?
What is a co-ordinate matrix?
A way of representing co-ordinates in a matrix, with all the co-ordinates top-down next to each other.
What is a transformation matrix?
A matrix which describes a transformation to a coordinate system.
What is the
\[2 \times 2\]identity matrix??
\[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}\]What is the
\[3 \times 3\]identity matrix??
\[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}\]How can you combine multiple transformation matrices?
Multiplying all the transformation matrices together.
How can you think of a transformation matrix?
As defining new, transformed values for the unit vectors $\hat{i}$ and $\hat{j}$.
The rule for matrices that $(A \times B) \times C = A \times (B \times C)$ is known as?
The Law of Associativity.
How is matrix multiplication different from normal multiplication?
It is not commutative.
What’s a way of describing something not being commutative?
What is the identity matrix?
The $m \times n$ matrix which does not change what it is multiplying.
What is the \(2 \times 2\) identity matrix?
What is the \(3 \times 3\) identity matrix?
What is the inverse matrix of a matrix?
A matrix that multiplies with the original matrix to give the $m \times n$ identity matrix.
2022-04-14
If you’ve been given that
\[\pmb{M}\pmb{M}^T = 4\pmb{I}\]how can you quickly work out the inverse matrix?? $$\pmb{M}^T$ must be equal to $4$ times the inverse matrix.