11)

Step 1:

The hypotenuse of a right angles triangle is longer than the longest of the two sides.

The shortest side is long.

Find the lengths of the sides.

Consider the right angle triangle,

Let longest side is and hypotenuse is

Right angle property is

\ \

Solution:

13)

Step 1:

The matrix is

i)

Find the detrminant.

Determinant value of the matrix is

iii)

The co factor of

The co factor of the

Solution:

Determinant value of the matrix is

The co factor of the

14)

Step 1:

 The system of equations are

Convert the equations into matrices form ,

where is coefficient matrix, is variable matrix and is constant matrix.

Solve the equations by using Cramers Rule.

Since Cramers Rule is applicable.

Step 2:

\ \

Solution:

The value of

15)

Step 1:

 The system of equations are

Convert the equations into matrices form ,

where is coefficient matrix, is variable matrix and is constant matrix.

Solve the equations by using Cramers Rule.

Since Cramers Rule is applicable. \ \

\ \

Step 2:

The co factor of

The co factor of the

Solution:

The value of

The co factor of the

18)

Step 1:

Find the two numbers.

Consider the two numbers are

The sum of two numbers is

The difference of their squares is

Rewrite the equation is

Solve the two equations

The two numbers are

Solution:

21)

Step 1:

The polar form is

Conversion from Polar to rectangular form :

and .

Substitute in the rectangular equation.

The rectangular form is 

Step 2:

De Moivres Theorem:

If is a complex number, then

where is a positive integer.

De Moivres theorem: .

Then,

Solution:

22)

Step 1:

 The system of equations are

Convert the equations into matrices form ,

where is coefficient matrix, is variable matrix and is constant matrix.

Solve the equations by using Cramer\\'s Rule.

Since Cramer\\'s Rule is applicable. \ \

\ \

Solution:

The value of