x1 = 1.0 

x1 = 1.6 

x1 = 0.8 

x1 = 1.4

x1 = 2.0 

Drawing lines through two points on the curve 

Finding the area under the curve

Finding the midpoint between two points

Drawing tangent lines to the curve 

Drawing perpendicular lines to the x-axis

E=2I−AB 

E=AB−I

E=B−A⁻¹

E=A⁻¹−B

E=2BA−I

To compute the determinant of the matrix.

To introduce zeros in the off-diagonal elements.

To compute the inverse of the matrix.

To factorize the matrix into lower and upper triangular matrices.

To scale the matrix elements.

xᵢ = det(Aᵢ) - det(A) 

xᵢ = det(A) × det(Aᵢ) 

xᵢ = |det(Aᵢ)| / |det(A)|

xᵢ = det(Aᵢ) / det(A)  

xᵢ = det(A) / det(Aᵢ) 

0.01

0.125

0.25

0.004

1.83 

3.0

2.5

2.17

2.0

To find eigenvalues of a symmetric matrix

To compute integrals using trapezoidal rule

To solve differential equations numerically

 To factorize large matrices efficiently

To approximate an unknown function using a polynomial that passes through given data points 

 h = (b - a)/5

 h = (b - a)/7

 h = (b - a)/3

 h = (b - a)/4

 h = (b - a)/6

The matrix must have all eigenvalues equal

The matrix must have a dominant eigenvalue

The matrix must be singular

The matrix must be diagonal