Matrices · Form 5
Matrices: Key Terms
The key Matrices terms you need for SPM Mathematics, defined plainly in English, Malay and Chinese.
- Matrix A rectangular array of numbers arranged in rows and columns.
- Determinant A number ad − bc found from a 2×2 matrix; if it is zero, the matrix has no inverse.
- Inverse matrix The matrix that, multiplied by the original, gives the identity; used to solve simultaneous equations.
- Identity matrix A square matrix with 1s on the diagonal and 0s elsewhere; it leaves a matrix unchanged when multiplied.
- Order of a matrix The number of rows by the number of columns, e.g. a 2×3 matrix.
- Scalar multiplication Multiplying every element of a matrix by the same number.
Term pairs students mix up
- Order vs determinant, the difference is: the order is the SIZE of a matrix, written rows × columns (e.g. 2×2); the determinant is a single NUMBER, ad − bc, that only a square matrix has.
- Identity matrix vs inverse matrix, the difference is: the identity I = [[1,0],[0,1]] leaves a matrix unchanged under multiplication; the inverse A⁻¹ is the specific matrix that multiplies with A to GIVE the identity.
- Determinant vs inverse, the difference is: the determinant is one number you compute first; the inverse is a whole matrix you build from it. The determinant is a gatekeeper, if it is zero, no inverse exists.
- Scalar multiplication vs matrix multiplication, the difference is: scalar multiplication multiplies every entry by one number; matrix multiplication combines two matrices by the row-into-column rule and needs the orders to match.
- Singular vs non-singular matrix, the difference is: a singular matrix has determinant zero and no inverse; a non-singular matrix has a non-zero determinant and a unique inverse.
How these terms are phrased in real SPM questions
SPM rarely uses the jargon head-on; it hides the term inside an instruction. 'Find the value of p such that the matrix has no inverse' is really asking you to set the determinant equal to zero, the phrase 'no inverse' signals a singular matrix.
'It is given that N is the inverse of M' means MN = I, so you can equate entries to find unknowns. 'Express as a single matrix' points to carrying out the addition, scalar or matrix multiplication until one array remains.
'Hence, using matrices, solve...' is the standard cue to write PX = B and apply X = P⁻¹B.
And an instruction naming a '2×2 matrix' is telling you the order, which means a determinant and inverse exist to be asked about.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What does 'singular matrix' mean if a question uses that phrase?
A singular matrix is one whose determinant equals zero, which means it has no inverse. If a question describes a matrix as singular, or asks for the value that makes it singular, it wants you to set ad − bc = 0 and solve.
The opposite, a non-singular matrix, has a non-zero determinant and one unique inverse.
What is a 'square matrix', and why does the chapter keep needing one?
A square matrix has an equal number of rows and columns, such as 2×2 or 3×3. Only square matrices have a determinant and an inverse, and only square matrices can equal the identity.
Because this chapter is built around the determinant and the inverse of a 2×2, almost every key operation quietly assumes the matrix is square.
When a matrix is written as 2×3, does the 2 mean rows or columns?
The first number is always the rows, the second the columns, so 2×3 means two rows and three columns. Reading the order correctly is what tells you whether two matrices can be multiplied: the columns of the first must equal the rows of the second, so the middle two numbers must agree.
Getting rows and columns the wrong way round breaks that check.