Matrices — Part 2: Operations and invertible matrices: visual lesson, ISC Class 12 Mathematics

Lesson

Matrices, Part 2

Arithmetic with whole tables of numbers at once.

In this lesson you will

Add, subtract and scale matrices
Multiply compatible matrices of order up to 3
Show that matrix multiplication is not commutative and that non-zero matrices can have a zero product
Decide whether a matrix is singular or non-singular
Verify and find inverses, and prove that an inverse is unique

Part 2 at a glance.

Concept

$A + B$ adds corresponding entries (same order needed); $kA$ multiplies every entry by $k$ .

Adding matrices adds corresponding entries.
Imagined Kochi bakery	Week 1	Week 2	Total
Bread, buns, cakes (shop A)	40, 25, 30	38, 30, 22	78, 55, 52
Bread, buns, cakes (shop B)	35, 20, 45	41, 18, 40	76, 38, 85

Concept

The $(i, j)$ entry of $AB$ is row $i$ of $A$ times column $j$ of $B$ : multiply in pairs and add.

(AB)_{ij} = \sum_k a_{ik} b_{kj}