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7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

Chapter 5, Problem 18RE

Textbook Problem

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In Exercises 17–20, write the given system of linear equations as a matrix equation, and solve by inverting the coefficient matrix.

Expert Solution

To determine

**To calculate:** The matrix equation of the system of linear equations and solve by inverting the coefficient matrix

**Given Information:**

The system of linear equations are

**Formula used:**

In the matrix equation *A* has entries equal to the coefficients of the left side of the system of equations and the matrix *X* is the column matrix of the unknowns in the system and the matrix *B* is the column matrix and has entries equal to the coefficients of the right side of the system of equations.

*I* is the

The two matrices *A* and *B* are equal if they have same dimensions, also their corresponding entries are equal.

For matrices *A* have dimension *B* have dimension *AB* is the matrix of dimension *ij*th entry of *AB* is the sum of product of corresponding entries of the row *i* of *A* and the column *j* of *B*.

**Calculation:**

Consider the system of linear equations,

Recall that in the matrix equation *A* has entries equal to the coefficients of the left side of the system of equations and the matrix *X* is the column matrix of the unknowns in the system and the matrix *B* is the column matrix and has entries equal to the coefficients of the right side of the system of equations.

Thus,

Hence, the matrix equation is

Solve the equation for *X*.

Consider the equation

Multiply both sides on the left of the equation by

Recall that *I* is the

Substitute

Thus, the equation is

Consider the matrix

Recall that a matrix with *m* rows and *n* columns is of dimension *m* and *n* are positive integers.

Since, number of rows in

Substitute *m* and *n* in

Thus, dimension of

Augment the matrix with the

Thus, the augmented matrix is

Row reduce the matrix

Perform the row operations

Perform the row operations

Perform the row operations

Thus,

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Remove the parentheses from each expression: a(b+c)

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All Pro Sports Center purchases $45,300 in baseball gloves from Spaulding on May 5. Spaulding allows 4/15, n/45...

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Calculus: Early Transcendental Functions (MindTap Course List)

Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. 35. f(x) = arctan (x2)

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Finding a Value In Exercises 5962, use the result of Exercise 51 to find such that RN 0.001 for the convergent ...

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5. In Example 3 of Section 3.1, find elements and of such that .
From Example 3 of section 3.1: and is a set...

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Trigonometry (MindTap Course List)

True or False
If the series converges to a number s, then all rearrangements of also converge to s.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

True or False:
If converges and converges, then converges.

Study Guide for Stewart's Multivariable Calculus, 8th

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In baseball, an earned run is any run that the opposing team scores off the pitcher except for runs scored as a...

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A full binary tree is a rooted tree in which .

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Perform all operations and express all answers in a+bi form. (511i)(5+11i)

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Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places bu...

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Express the following decimal numbers as BCD (8421) numbers. 73

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Calculus Volume 2

25. Given below is a bivariate distribution for the random variables x and y.
f(x, y) x y
.2 50 80
.5 30 50
.3 ...

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In Exercises 20 and 21, describe the transformations of the graph of f that yield the graph of g. fx=2.2x,gx=2....

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