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Write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix.
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Ch. 6 - Matrices and Determinants
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 7, Problema 31
Write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix.
Guida verificata passo dopo passo1
Identify the variables and write them as a column matrix \(X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}\).
Extract the coefficients of the variables from each equation to form the coefficient matrix \(A = \begin{bmatrix} 1 & 3 & 4 \\ 1 & 2 & 3 \\ 1 & 4 & 3 \end{bmatrix}\).
Write the constants from the right side of each equation as the constant matrix \(B = \begin{bmatrix} -3 \\ -2 \\ -6 \end{bmatrix}\).
Express the system of equations in the matrix form $AX = B$, where \(A\) is the coefficient matrix, \(X\) is the variable matrix, and \(B\) is the constant matrix.
The final matrix equation is \(\begin{bmatrix} 1 & 3 & 4 \\ 1 & 2 & 3 \\ 1 & 4 & 3 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -3 \\ -2 \\ -6 \end{bmatrix}\).
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Systems of Linear Equations
A system of linear equations consists of multiple linear equations involving the same set of variables. The goal is to find values for the variables that satisfy all equations simultaneously. Understanding how to represent and solve these systems is fundamental in algebra.
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Introduction to Systems of Linear Equations
Matrix Representation of Linear Systems
A system of linear equations can be expressed in matrix form as AX = B, where A is the coefficient matrix containing the coefficients of variables, X is the column matrix of variables, and B is the constant matrix. This form simplifies solving and analyzing the system.
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4:27Introduction to Systems of Linear Equations
Coefficient and Constant Matrices
The coefficient matrix (A) includes all coefficients of the variables arranged by equation and variable order, while the constant matrix (B) contains the constants from the right side of each equation. Correctly identifying these matrices is essential for forming the matrix equation.
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4:35Introduction to Matrices
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