Matrices · 2.1.3
Equal matrices
Two matrices are equal only when they have the same order (same number of rows and columns) and every corresponding element matches exactly. Students must compare both order and all element pairs, and can use this idea to solve for unknown letters used inside matrices.
The official learning standard (2.1.3)
“Determine whether two matrices are equal.”
What it means
Two matrices are equal only when they have the same order (same number of rows and columns) and every corresponding element matches exactly. Students must compare both order and all element pairs, and can use this idea to solve for unknown letters used inside matrices.
How it is examined
Paper 1 objective items ask students to identify or verify equal matrices from given options. Paper 2 structured questions often use equal matrices to set up a system of simple equations, which students then solve to find unknown letters used as matrix elements.
Worked example
Given that [[x, 3], [2, y]] = [[5, 3], [2, -4]], find the values of x and y.
- Since the matrices are equal, corresponding elements must be equal.
- Compare position (1,1): x = 5.
- Compare position (2,2): y = -4.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What are the two conditions for matrices to be equal?
Both matrices must have the same order (same number of rows and columns), and every element in the same position must be identical. If either condition fails, different order or even one mismatched element, the two matrices are not equal.
Can I use matrix equality to solve for unknowns?
Yes, this is a common SPM technique. Set corresponding elements of two equal matrices equal to each other to form simple equations, then solve those equations individually to find the unknown letters used as matrix elements.
Are [[1,2]] and [[1],[2]] equal?
No, these matrices have different orders, the first is a 1×2 row matrix, the second is a 2×1 column matrix. Even though they contain the same numbers, different orders mean they can never be equal under the definition of matrix equality.