# 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:

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.

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

• 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.

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

• 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.

• Gaussian elimination and ……………methods.

• Which of the following method is not an iterative method?

1. 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.

• Which of the following method is not an iterative method?

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

• 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.

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

• While using power method, from the resultant normalize vector
u(2)=11.4817⎛⎝⎜⎜0.3981760.8212671.0⎞⎠⎟⎟

we have the largest eigen value and the corresponding eigenvector as

• How many Eigen values will exist corresponding to the function; Exp(ax) = e^ax, when the matrix operator is of differentiation?

• While using Gaussian Elimination method, which of the following augmented matrix is in upper triangular form?

• Which of the following systems of linear equations has a strictly diagonally dominant coefficient matrix?

2

1

2

7

2

1

1

33
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