## 1.7 Problem solving with Matrices

**Multiplying matrices**

Two matrices can only be multiplied if their inner

dimensions are the same.

For ex- if matrix A has dimensions (5* 4) and matrix B has dimensions (4*1),

then the resulting matrix C would have the dimension (5*1) when both the matrices are multiplied.

1.7 Problem solving with Matrices - MDM4U1@FMG

Identity Matrix

Identity matrix have entries of 1 along the main diagonal and zeroes for all other entries.

1.7 Problem solving with Matrices - MDM4U1@FMG

Inverse Matrix

1.7 Problem solving with Matrices - MDM4U1@FMG

NOTE:-

* A^-1 ≠ 1/A

* ad ≠ bc, since it would require dividing by zero.

Property of inverse matrix

If a matrix ‘A’ is multiplied with its inverse matrix ‘A^-1’ , then we would get back the identity matrix'I' discussed before.

1.7 Problem solving with Matrices - MDM4U1@FMG

1.7 Problem solving with Matrices - MDM4U1@FMG

Network Matrix:-

Matrices are also used to show transport and communication links between two or more places.

Such matrices are called Network Matrices.

These matrices provide information on the number of direct links between two vertices or points (such as people or places).

A direct link is denoted by ‘1’ whereas an indirect link is denoted by ‘0’. The following example shows this more clearly:-

1.7 Problem solving with Matrices - MDM4U1@FMG

1.7 Problem solving with Matrices - MDM4U1@FMG

References

Mathematics of Data Management , Grade 12, (MDM4U). McGraw-Hill Ryerson