]]>The first row of the augmented matrix of the system of linear equations is: 2x+z=4 x-y+z=-3 -y+z=-5

If there are three equations in two variables, then which of the following is true?

Dependent Systems of Equations with Three Variables

We know from working with systems of equations in two variables that a dependent system of equations has an infinite number of solutions. The same is true for dependent systems of equations in three variables. An infinite number of solutions can result from several situations. The three planes could be the same, so that a solution to one equation will be the solution to the other two equations. All three equations could be different but they intersect on a line, which has infinite solutions (see below for a graphical representation). Or two of the equations could be the same and intersect the third on a line (see the example problem for a graphical representation).

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@zaasmi said in MTH603 Quiz 1 Solution and Discussion:

If there are three equations in two variables, then which of the following is true?

A system of equations in three variables involves two or more equations, each of … Plug in these values to each of the equations to see that the solution satisfies all … when graphing each equation in the system and then finding the intersection point of … A three dimensional box with three slanted planes crossing through it.

Explanation:

The simple answer is yes.

If you have two consistent equations and they are linearly independent, then you will have to assign arbitrary values to one of the variables. If you have two consistent equations and they are linearly dependent, then you will have to assign arbitrary values to two of the variables, both cases lead to an infinite number of solutions. If they inconsistent, then obviously there is no solution.

Graphically two consistent linearly independent equations will form 2 planes in

R

3

that intersect and all solutions will lie on the line of intersection leading to an infinite number of solutions.

Two consistent linearly dependent equations will just be a single line in

R

3

and all solutions will lie on this line, leading to an infinite number of solutions.

If the two equations are inconsistent then you will have 2 parallel lines in

R

3

, and no point of intersection, hence no solutions.

If there are three equations in two variables, then which of the following is true?

A system of equations in three variables involves two or more equations, each of … Plug in these values to each of the equations to see that the solution satisfies all … when graphing each equation in the system and then finding the intersection point of … A three dimensional box with three slanted planes crossing through it.

]]>The statement, 7265 instead of 7269 lies in the category of:

With regard to the dangers from lead opinion , if you removed the loose paint off the hands poisoning , it is pretty hard on … Do you not think your statement is rather a 7269. … That 7265. Of course they will not need soap if they can is where sand - papering comes in . rub the paint off dry from their hands P - I said you 7293.

]]>Gaussian elimination and ……………methods.

In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of operations performed on the corresponding matrix of coefficients.

]]>Which of the following method is not an iterative method?

- Which of the following is not an iterative method?

Explanation: Jacobi’s method, Gauss Seidal method and Relaxation method are the iterative methods and Gauss Jordan method is not as it does not involves repetition of a particular set of steps followed by some sequence which is known as iteration.

The number system that is used in our daily life is called…system.

The number system that we use in our day-to-day life is the decimal number system. Decimal number system has base 10 as it uses 10 digits from 0 to 9.

]]>u(2)=11.4817⎛⎝⎜⎜0.3981760.8212671.0⎞⎠⎟⎟

we have the largest eigen value and the corresponding eigenvector as

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The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite matrices. Explanation: Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices because only in this case convergence is possible.

]]>The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

The Jacobi method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal (Bronshtein and Semendyayev 1997, p. 892). Each diagonal element is solved for, and an approximate value plugged in. The process is then iterated until it converges.

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