Mathematical Formulas for Industrial and Mechanical Engineering

‘ The matrix of cofactors is

218 5

1 263

1321

2

4

3

5

, hence

AdjðAÞ5

211 21

8 262

253 21

2

4

3

5

.

Now

A

21

5

1

A

jj

AdjðAÞ5

1

ð22Þ

211 21

8 262

253 21

2

4

3

5

5

1=2 21=21=2

243 21

5=2 23=2 21

2

4

3

5

‘A

21

5

1

2

2

1

2

1

2

243 21

5

2

2

3

2

1

2

2

6

6

6

6

6

6

4

3

7

7

7

7

7

7

5

3.10 System of Linear Equations

G

An equation of the form ax 1 by 1 c 5 0, where at least one of the real numbers a and b

is not zero, is called a linear equation in x and y. Similarly, an equation of the form

ax 1 by 1 cz 1 d 5 0 is a linear equation in three variables x, y, and z.

G

A system of equations can have exactly one solution, no solution, or an infinite number

of solutions. A system with at least one solution is called a consistent system.