Linear algebra study
Introduction :
A linear algebra is the sub division of algebra which maintain the relationship with the families of vectors called vector spaces or linear spaces, and the equation contains one input vector and output another vector, according to certain rules. The basic function of linear algebra is to find the solution of systems of linear expressions with the reference of some known variables. Linear algebra has the demonstration in analytic geometry and operator theory. The following are the example problems for linear algebra study.
Linear relationship example problems for study:
The example problems given below with detailed solution for study.
Example 1:
Solve the linear algebraic equation -2(y - 1) – 4y - 1 = 3(y + 2) – 2y
Solution:
Given expression is
-2(y - 1) – 4y - 1 = 3(y + 2) – 2y
Multiplying the integer terms
-2y + 2 – 4y - 1 = 3y + 6 – 2y
Grouping the above terms
-6y + 1 = y + 6
Subtract 1 on both sides
-6y + 1 - 1 = y + 6 -1
Group the above terms
-6y = y + 5
Subtract y on both sides
-6y - y = y + 5 -y
Group the above terms
-7y = 5
Multiply -1/7 on both sides
y = - 5/7
y = - 5/7 is the solution.
Example 2:
Solve the linear algebraic equation -4(y + 2) = y + 9
Solution:
Given expression is
-4(y + 2) = y + 9
Multiplying the integer terms
-4y - 8 = y + 9
Add 8 on both sides
-4y - 8 + 8 = y + 9 + 8
Grouping the above terms
-4y = y + 17
Subtract y on both sides
-4y - y = y + 17 -y
Grouping the above perms
-5y = 17
Multiply -1/5 on both sides
y = -17/5
y = -17/5 is the solution.
Linear relationship practice problems for study:
1) Solve the linear algebraic equation -3(y - 2) – 2y - 3 = 2(y + 1) – 4y
Answer: y = 1/3 is the solution. 2) Solve the linear algebraic equation -2(y + 3) = y + 6
Answer: y = -4 is the solution.
I like to share this Linear Equation with you all through my blog.
A linear algebra is the sub division of algebra which maintain the relationship with the families of vectors called vector spaces or linear spaces, and the equation contains one input vector and output another vector, according to certain rules. The basic function of linear algebra is to find the solution of systems of linear expressions with the reference of some known variables. Linear algebra has the demonstration in analytic geometry and operator theory. The following are the example problems for linear algebra study.
Linear relationship example problems for study:
The example problems given below with detailed solution for study.
Example 1:
Solve the linear algebraic equation -2(y - 1) – 4y - 1 = 3(y + 2) – 2y
Solution:
Given expression is
-2(y - 1) – 4y - 1 = 3(y + 2) – 2y
Multiplying the integer terms
-2y + 2 – 4y - 1 = 3y + 6 – 2y
Grouping the above terms
-6y + 1 = y + 6
Subtract 1 on both sides
-6y + 1 - 1 = y + 6 -1
Group the above terms
-6y = y + 5
Subtract y on both sides
-6y - y = y + 5 -y
Group the above terms
-7y = 5
Multiply -1/7 on both sides
y = - 5/7
y = - 5/7 is the solution.
Example 2:
Solve the linear algebraic equation -4(y + 2) = y + 9
Solution:
Given expression is
-4(y + 2) = y + 9
Multiplying the integer terms
-4y - 8 = y + 9
Add 8 on both sides
-4y - 8 + 8 = y + 9 + 8
Grouping the above terms
-4y = y + 17
Subtract y on both sides
-4y - y = y + 17 -y
Grouping the above perms
-5y = 17
Multiply -1/5 on both sides
y = -17/5
y = -17/5 is the solution.
Linear relationship practice problems for study:
1) Solve the linear algebraic equation -3(y - 2) – 2y - 3 = 2(y + 1) – 4y
Answer: y = 1/3 is the solution. 2) Solve the linear algebraic equation -2(y + 3) = y + 6
Answer: y = -4 is the solution.
I like to share this Linear Equation with you all through my blog.