Solving Linear Systems of Equations in Dependence and Matrices

1. INDEPENDENT LINEAR SYSTEM

a. a system with exactly one solution
b. an equation that is satisfied by every real number
c. equations that are identical
d. a system of lines

2. DEPENDENT SYSTEM

a. a system that is independent
b. a system that depends on a variable
c. a system that has no solution
d. a system for which the graphs coincide

3. ADDITION METHOD

a. adding the same number to each side of an equation
b. adding fractions
c. eliminating a variable by adding two equations.
d. the sum of a number and its additive inverse is zero.

a. the length of a matrix
b. the number of rows and columns in a matrix
c. the highest power of a matrix.
d. the lowest power of a matrix.

Can you show me how to solve the following problems by the substitution method. Can you indicate whether each system is INDEPENDENT, INCONSISTENT, or DEPENDENT.

1. x=1/8 y - 1

y=1/4x+ 39

2. -3x+ y=3
2x-3y=5

Thank you for your much needed HELP !!!

Solution Summary

Solving Linear Systems of Equations is investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

Mathematical modeling using systems of linear first order equations. ...Solving this system of equations gives: C1=1/12 and C2=-1/12 The solution is then,. ...

... rank of matrix A can not be more than 3. To prove that other 3 columns are linearly independent, we need to solve a system of linear equations (A*x=0) and ...

... Determine if the homogenous linear systems below 5. have non-trivial ... c) By the back-substitution, the solution is ... For example, the system x + y = 2 and x − y ...

... To prove that other 3 columns are linearly independent, we need to solve a system of linear equations (A*x=0) and if its only solution is x=0, then the 3 ...

... The expert examines the systems of linear equations in ... Thus, the solution space consists of the entire ... what is meant by a dependent system of linear equations. ...

... However, not all systems of linear equations have unique ... when solving a system of linear equations using matrices. ... that means our system has a unique solution: ...

... Examine for example the system of linear equations: ... This indicates that only systems of equations that have a solution have an inverse matrix. ...

... we set the first equation: (1.6) Solving the system: ... have (otherwise we get the trivial solution) (1.7) This ... that again we get a linear dependent system and we ...

... denote: ( 22) The solution of this system is almost ... way to represent the above solution which will ... to , and and making a linear combination: ( 24 ...

... Y=a+bx, So, we need to determine the coefficients a and b so we have to solve for an equations system for a and b. Hence, the use of linear algebra make ...