Linear Algebra Toolkit
Introduction :
Algebra is a branch of mathematics, we use letters like a, b, x and y to denote numbers. Performing addition, subtraction, multiplication, division or extraction of roots on these symbols and real numbers, linear algebra is unique, emphasis and computational skills we see what are called algebraic expressions. The following are some examples of algebraic expressions 2x + 3, (3a + b) (2x – y).
Methods of Solving Liner Equations in One Variable – linear algebra toolkit:
For Solving a linear equation of one variable the following rules are used which do not change the equation. Let us see them. They are :
- Both the sides of an equation add the same number
- Both the sides of an equation subtract the same number
- Both the sides of an equation multiply the same number
- Both the sides of an equation subtract the same number
Examples – – linear algebra toolkit:
Examples – linear algebra tool kit:
- Solve for x: x – 6= 10
Solution:
x – 6 = 10
Add 6 to both side of the equation
x- 6 + 6= 10 + 6
x = 16
The answer x is 16
- Solve for y: y + 8 = 15
Solution:
y + 8 = 15
Subtract 8 from both sides of the equation
y + 8 – 8 = 15 – 8
y = 7
The answer y is 7.
- Solve for x: x – 1/2 = 5/2
Solution:
x – 1/2 = 5/2
Add 1/2 to both sides of the equation
x = 5/2 + 1/2
x = 6/2
x = 3
The answer x is 3
- Solve for x: 5 x – 6 = 3 x – 10
Subtract 3x from both sides of the equation
5x – 3x – 6 = 3x – 3x – 10
2x – 6 = – 10
Add 6 to both sides of the equation
2x – 6 + 6 = – 10 + 6
2x = – 4
Divided by 2 both side of the equation
x = – 2
The answer x is – 2
- Solve for x: 4 x – 6 = 12 x – 40
Solution:
4 x – 6 = 12 x – 40
Subtract 4x from both sides of the equation:
4x – 4x – 6 = 12x – 4x – 40
6 = 8x – 40
Add 40 to both sides of the equation
-6 + 40 = 8x – 40 + 40
36 = 8x
Divided by 8 both side of the equation
x = 4.5
The answer x is 4.5
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- Solve for x: x – 8= 10
Solution:
x – 8 = 10
Add 6 to both side of the equation
x- 8 + 8= 10 + 8
x = 18
The answer x is 18
- Solve for x: x – 5= 10
Solution:
x – 5 = 10
Add 6 to both side of the equation
x- 5 + 5= 10 + 5
x = 15
The answer x is 15.
I am planning to write more post on dividing rational expressions solver with example, Standard Deviation Calculation. Keep checking my blog.
Procedure of solving three given linear equations in x, y, z – linear algebra toolkit:
- Three equations are given.
- Take any two say the first two equations.
- Eliminate one variable say z.
- Similarly eliminate z from the second and the third (or first and the third equation).
- We get two linear equations in x, y.
- Solve them in the usual way learnt in earlier cases.
- Substitute the values of x and y in any one of the three equations to get the value of z.
- Thus the values of x, y and z are obtained.
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