subject: Advanced Algebra: [print this page] Advanced algebra deals with algebraic geometry, number theory, commutative algebra and non commutative algebra. Advance version of the algebra is known as advanced algebra. Advanced algebra also used for factorizing the equations. It is also used for solving three variable linear equations. Topics under advanced algebra is given below,
Linear equations and non linear equations
Quadratic equations
Word problems
Factorization
Example Problems for Advanced Algebra
Problem 1:
Solve the system of algebraic equations
x + 2y - z = 3.
2x -2y + 3z = 8.
- x + y + z = 6.
Solution:
x + 2y - z = 3 (1)
2x - 2y + z = 0 (2)
- x + y + z = 6 (3)
First add equation (1) and equation (3)
x + 2y - z = 3
-x + y + z = 6
3y = 9
Divide by 3 on both sides
y = 3.
Plug y = 3 in equation (1)
x + 6 - z = 3
z = 3 + x (4)
Plug y value in equation (2)
2x - 6 + z = 0
z = 6 - 2x (5)
Equating equation 4 and equation 5
3 + x = 6 - 2x
x = 1.
Plug x = 1 and y = 3 in equation (1)
1 + 6 - z = 3
z = 4
Answer:
The final answer is x = 1, y = 3, z = 4.
Problem 2:
Solve and Factorize the equation
x2 - 5x + 6 = 0.
Solution:
x2 - 5x + 6 = 0.
Factoring the above equation
x2 - 2x - 3x + 6 = 0
x (x- 2) - 3 (x - 2) = 0
(x - 2) (x- 3) = 0
Equating each factor value to zero
x = 2, x = 3.
Answer:
The factor for the above equation is x = 2, x = 3.
Practice Problem for Advanced Algebra
Problem 1:
Solve the advanced algebraic equation
x - y + z = 3
2x + y - 3z = - 7
x + 2y - z = 5
Answer:
The final answer is x = 2, y = 4, z = 5.
Problem 2:
Solve the advanced algebraic equation
2x - y + 3z = 11
x + y - z = 2
3x + y + 2z = 14
Answer:
The final answer is x = 3, y = 1, z = 2.
Problem 3:
Solve and factorize the equation 2x2 + 12x + 16 = 0
Answer:
The final answer is x = - 4, x = - 8.
Problem 4:
Solve and factorize the given equation x2 - 7x + 12 = 0
Algebra is the subdivision of math which deals with the motion problems also the study of system of operations and relations, the concepts & constructions derived from them, including polynomials, algebraic structures and equations, along with analysis, topology, geometry, and number theory. It is not only applied in math, but also in almost every field to perform certain operations. Motion problems are a type of word problem which involves with rate, distance and time. Here we see about motion problems in detail.
Formulae Used in Solving Algebra Motion Problems:
The basic formulae used to solve algebra problems on motions is,
