Question

Exercise 2 Describe all values of $a, b, c \in \mathbb{R}$ such that the following system of linear equations is inconsistent. $\begin{cases} x_1 - x_2 + 2x_3 = a \\ 2x_1 + 4x_2 - 3x_3 = b \\ 4x_1 + 2x_2 + x_3 = c \end{cases}$

          Exercise 2
Describe all values of $a, b, c \in \mathbb{R}$ such that the following system of linear equations is inconsistent.
$\begin{cases} x_1 - x_2 + 2x_3 = a \\ 2x_1 + 4x_2 - 3x_3 = b \\ 4x_1 + 2x_2 + x_3 = c \end{cases}$

Exercise 2
Describe all values of a, b, c ∈ℝ such that the following system of linear equations is inconsistent.
x1 - x2 + 2x3 = a
2x1 + 4x2 - 3x3 = b
4x1 + 2x2 + x3 = c

Added by Audrey M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

03/03/2023

Step 1

The given system of equations can be written in matrix form as: \[ \begin{bmatrix} 1 & -1 & 2 \\ 2 & 4 & -3 \\ 4 & 2 & 1 \\ \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ \end{bmatrix} = \begin{bmatrix} a \\ b \\ c \\ \end{bmatrix} \] Show more…

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Exercise2 Describe all values of a, b, c E IR such that the following system of linear equations is inconsistent. x1-x2+2x3=a 2x1+4x2-3x3=b 4x1+2x2+x3=c