Read a labelled data matrix
Rows and columns can represent different variables, so each cell is identified by two labels. A row total is found across a row, while a column total is found down a column
\[\text{row total} = \text{sum across a row},\quad \text{column total} = \text{sum down a column}\]
- Match the two labels Use the row label and column label together to locate one cell \(\displaystyle \text{position of }A_{12}=(1,2)\)
- Add across a row A row category total uses every data entry in that row \(\displaystyle 8+5+7=20\)
- Add down a column A column category total uses every data entry in that column \(\displaystyle 8+4=12\)
- Count data rather than headings Labels identify entries but are not included in a numerical total \(\displaystyle \text{total}=8+5+7=20\)
Worked example
The rows of a data matrix are North and South, and the columns are Week 1, Week 2 and Week 3. The rows are [6, 3, 8] and [5, 7, 4]. Find the North value for Week 2 and the South row total
\[A=\begin{bmatrix}6&3&8\\5&7&4\end{bmatrix}\]
- \(\displaystyle A_{12}=3\)North is row 1 and Week 2 is column 2, so their cell contains 3
- \(\displaystyle \text{South row}=[5\quad7\quad4]\)South is the second row of the matrix
- \(\displaystyle 5+7+4=16\)Add the three entries across the South row
- \(\displaystyle \text{South total}=16\)The South row total is 16
Common mistakes
Adding along the wrong axis
✕\(\displaystyle \text{North total}=6+5=11\)✓\(\displaystyle \text{North total}=6+3+8=17\)
In the worked example's matrix A, North is the first row [6, 3, 8]. Add across that row, not down the Week 1 column [6, 5]Transposing an element address
✕\(\displaystyle A_{12}=5\)✓\(\displaystyle A_{12}=3\)
In the worked example's matrix A, North in Week 2 is row 1, column 2 and contains 3. The value 5 belongs to row 2, column 1, so A12 and A21 are different cellsReturning an address instead of a value
✕\(\displaystyle A_{12}=(1,2)\)✓\(\displaystyle A_{12}=3\)
In the worked example's matrix A, (1, 2) is the address of the cell, not its value. The answer to the value question is the entry 3 stored thereDifficulty levels
introRead one value and one total from a small labelled data matrix
standardFind row and column totals and locate a requested labelled cell
challengeHandle a changed axis presentation and find grand totals or the largest category
examChoose the correct total or leading category from alternatives with axis and address errors
Questions about this topic
What does one cell in a labelled matrix represent?+
It represents the data for the row category and column category that meet at that cell
How is a row total different from a column total?+
A row total adds entries horizontally across one row. A column total adds entries vertically down one column
Why must the row and column labels be read separately?+
They can describe different variables, so changing either label can select a different cell and a different meaning
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 12, VCE Units 3 & 4, General Mathematics, chapter 10: Matrices
In this chapter
State the order of a matrix and locate its elementsIdentify row, column, square, symmetric and zero matricesRead information from a labelled data matrixRead, transpose and classify a matrixConstruct a matrix from labelled information or an entry rule10A Matrix notation, types and construction: Solve a matrix equation10A Matrix notation, types and construction: Construct, apply and invert a permutation matrixAdd and subtract matricesFind unknown entries in a matrix equationMultiply a matrix by a scalarCombine scalar multiples of matrices10B Linear operations on matrices: Determine whether an inverse exists and calculate itDecide whether a matrix product is defined and give its orderMultiply matricesEvaluate powers of a square matrixIdentify and construct the identity matrix10C Matrix products, powers and permutations: Construct, apply and invert a permutation matrixFind the determinant of a 2 × 2 matrixFind the inverse of a 2 × 2 matrixWrite simultaneous equations as a matrix equationSolve simultaneous equations using the inverse matrix10D Determinants, inverses and matrix equations: Determine whether an inverse exists and calculate it10D Determinants, inverses and matrix equations: Solve a matrix equationUse matrix multiplication to answer an application questionUse row and column matrices of ones to extract totalsRepresent a network in a matrixIdentify the network a connection matrix describesInterpret connection sums and symmetryCount routes using powers of a connection matrixConstruct and analyse relation matrices