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Chapter 9: Problem 62

If you could use only one method to solve linear systems in three variables, which method would you select? Explain why this is so.

Short Answer

Expert verified
The most preferred method to solve linear systems in three variables would be to use matrices due to the reasons of reduced algebraic errors, clear visual representation and scalability for large systems.

Step by step solution

01

Choose a method

For this task, we will select the matrix method. The matrix method, in general, is a convenient way to handle and solve systems of linear equations. Matrices allow the convenient manipulation of coefficients and make the algebraic solution much more straightforward compared to other methods.
02

Explain the reasons

This method is selected because of the following reasons: 1. It does not require you to explicitly solve for one variable in terms of others, hence reducing the potential for algebraic errors. 2. It provides a clear visual representation of the coefficients of the variables, which can lead to better understanding of the system. 3. This method is scalable for large systems of equations.

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Most popular questions from this chapter

Find (if possible) the following matrices: a. \(A B\) b. \(B A\) $$ A=\left[\begin{array}{rrrr} {2} & {-1} & {3} & {2} \\ {1} & {0} & {-2} & {1} \end{array}\right], \quad B=\left[\begin{array}{rr} {-1} & {2} \\ {1} & {1} \\ {3} & {-4} \\ {6} & {5} \end{array}\right] $$

Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $$ \left\\{\begin{aligned} 3 a+b-c &=0 \\ 2 a+3 b-5 c &=1 \\ a-2 b+3 c &=-4 \end{aligned}\right. $$

Let $$ \begin{aligned} A &=\left[\begin{array}{cc} {1} & {0} \\ {0} & {1} \end{array}\right], \quad B=\left[\begin{array}{rr} {1} & {0} \\ {0} & {-1} \end{array}\right], \quad C=\left[\begin{array}{rr} {-1} & {0} \\ {0} & {1} \end{array}\right] \\ D &=\left[\begin{array}{rr} {-1} & {0} \\ {0} & {-1} \end{array}\right] \end{aligned} $$ Find the product of the difference between A and B and the sum of C and D.

Explaining the Concepts What is the difference between Gaussian elimination and Gauss-Jordan elimination?

Find (if possible) the following matrices: a. \(A B\) b. \(B A\) $$ A=\left[\begin{array}{ll} {2} & {4} \\ {3} & {1} \\ {4} & {2} \end{array}\right], \quad B=\left[\begin{array}{rrr} {3} & {2} & {0} \\ {-1} & {-3} & {5} \end{array}\right] $$
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