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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
Capitolo 7, Problema 55

In Exercises 55–56, write the system of linear equations for which Cramer's Rule yields the given determinants.

Guida verificata passo dopo passo
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Step 1: Understand that the determinant D corresponds to the coefficient matrix of the system of linear equations. The matrix for D is given as \( \begin{bmatrix} 2 & -4 \\ 3 & 5 \end{bmatrix} \). This means the system has two variables, say \( x \) and \( y \), and the coefficients of these variables in the two equations are from this matrix.
Step 2: The determinant \( D_x \) is formed by replacing the first column of the coefficient matrix with the constants from the right-hand side of the equations. The matrix for \( D_x \) is \( \begin{bmatrix} 8 & -4 \\ -10 & 5 \end{bmatrix} \). This tells us the constants on the right side of the equations are 8 and -10 respectively.
Step 3: Write the system of linear equations using the coefficients from matrix D and the constants from the right side. The first equation uses the first row of D: \( 2x - 4y = 8 \). The second equation uses the second row of D: \( 3x + 5y = -10 \).
Step 4: Verify that the system is consistent with the determinants given. The determinant D should not be zero for Cramer's Rule to apply, and the determinants D and \( D_x \) correspond to the coefficient matrix and the matrix with the first column replaced by constants, respectively.
Step 5: Summarize the system of equations as: \( \begin{cases} 2x - 4y = 8 \\ 3x + 5y = -10 \end{cases} \). This is the system for which Cramer's Rule yields the given determinants.

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