Q69E Question:聽Solve the linear syst... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 1: Q69E (page 39)

Question:Solve the linear system
$| \begin{matrix} y + z = a \\ X & + z = b \\ x + y & = C \end{matrix} |$ , where a,b andcare arbitrary constants.

Short Answer

Expert verified

Answer:

The solution of the linear system is $|\begin{matrix} y + z = a \\ y + z = b \\ y + y = c \end{matrix}|, x = \frac{b + c - a}{2}, y = \frac{a + c - b}{2}, z = \frac{a + b - c}{2}$ ,

Step by step solution

Consider the system

Consider the linear system.

$\begin{matrix} y + z = a \\ y + z = b \\ y + y = c \end{matrix}$

The matrix form of the system is,

$[\begin{matrix} 0 & 1 & 1 & | & 1 \\ 1 & 0 & 1 & | & b \\ 1 & 1 & 0 & | & c \end{matrix}]$

Step 2: Compute the system.

Consider the matrix,

$[\begin{matrix} 0 & 1 & 1 & | & 1 \\ 1 & 0 & 1 & | & b \\ 1 & 1 & 0 & | & c \end{matrix}]$

Perform the row reduction operation.

$[\begin{matrix} 0 & 1 & 1 & | & 1 \\ 1 & 0 & 1 & | & b \\ 1 & 1 & 0 & | & c \end{matrix}] ~ [\begin{matrix} 0 & 1 & 1 & 1 \\ 1 & 0 & 1 & b \\ 1 & 1 & - 2 & c - b - a \end{matrix}] [\begin{matrix} 1 & 0 & 0 & \frac{b - a + c}{2} \\ 0 & 1 & 0 & \frac{a - b + c}{2} \\ 0 & 0 & 1 & \frac{a + b - c}{2} \end{matrix}]$

The values are, $x = \frac{b + c - a}{2}, y = \frac{a + c - b}{2}, z = \frac{a + b - c}{2}$

Hence, $|\begin{matrix} y + z = a \\ y + z = b \\ y + y = c \end{matrix}|,$ $, x = \frac{b + c - a}{2}, y = \frac{a + c - b}{2}, z = \frac{a + b - c}{2}$ is the solution of the linear system, .

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91影视

Question:Solve the linear system
$| \begin{matrix} y + z = a \\ X & + z = b \\ x + y & = C \end{matrix} |$ , where a,b andcare arbitrary constants.

Short Answer

Step by step solution

Consider the system

Step 2: Compute the system.

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91影视

Question:Solve the linear system|y+z=aX+z=bx+y=C|, where a,b andcare arbitrary constants.

Short Answer

Step by step solution

Consider the system

Step 2: Compute the system.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Statistics

Calculus

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Question:Solve the linear system
$| \begin{matrix} y + z = a \\ X & + z = b \\ x + y & = C \end{matrix} |$ , where a,b andcare arbitrary constants.