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Ch. 6 - Matrices and Determinants
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 6 - Matrices and DeterminantsProblema 5
Capitolo 7, Problema 5

Write the augmented matrix for each system of linear equations.
{5x−2y−3z=0x+y=52x−3z=4\(\begin{cases}\) 5x - 2y - 3z = 0 \\ x + y = 5 \\ 2x - 3z = 4 \(\end{cases}\)

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1
Identify the coefficients of each variable in each equation. For the first equation \(5x - 2y - 3z = 0\), the coefficients are 5 for \(x\), -2 for \(y\), and -3 for \(z\).
For the second equation \(x + y = 5\), note that \(z\) is missing, so its coefficient is 0. The coefficients are 1 for \(x\), 1 for \(y\), and 0 for \(z\).
For the third equation \(2x - 3z = 4\), note that \(y\) is missing, so its coefficient is 0. The coefficients are 2 for \(x\), 0 for \(y\), and -3 for \(z\).
Write the augmented matrix by placing the coefficients of \(x\), \(y\), and \(z\) in columns, and the constants on the right side as the augmented part. The matrix will have three rows corresponding to the three equations.
The augmented matrix will look like this: \[\left[\begin{array}{ccc|c} 5 & -2 & -3 & 0 \\ 1 & 1 & 0 & 5 \\ 2 & 0 & -3 & 4 \end{array}\right]\]

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