Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
To find [tex]\(\left|A_y\right|\)[/tex] in the context of the given matrix equation and options, we need to understand that [tex]\(\left|A_y\right|\)[/tex] represents the determinant of the matrix formed by replacing the second column of the coefficient matrix [tex]\(A\)[/tex] with the constants from the right-hand side of the equation.
The system of equations given is:
[tex]\[ \begin{cases} 12x - 13y = 7 \\ 17x - 22y = -51 \end{cases} \][/tex]
The coefficient matrix [tex]\(A\)[/tex] is:
[tex]\[ A = \begin{pmatrix} 12 & -13 \\ 17 & -22 \end{pmatrix} \][/tex]
The constants matrix is:
[tex]\[ \mathbf{b} = \begin{pmatrix} 7 \\ -51 \end{pmatrix} \][/tex]
To find [tex]\(\left|A_y\right|\)[/tex], we replace the second column of [tex]\(A\)[/tex] with [tex]\(\mathbf{b}\)[/tex]:
1. Start with possible replacements from the given options to construct the matrices.
[tex]\(\begin{pmatrix} 7 & -13 \\ -51 & -22 \end{pmatrix}\)[/tex]
2. Calculate the determinant:
[tex]\[ \left| \begin{pmatrix} 7 & -13 \\ -51 & -22 \end{pmatrix} \right| = (7 \cdot -22) - (-13 \cdot -51) = -154 - 663 = -817 \][/tex]
Following this result, let's analyze the determinants from the remaining options:
[tex]\[ \left| \begin{pmatrix} 12 & 7 \\ 17 & -51 \end{pmatrix} \right| = (12 \cdot -51) - (7 \cdot 17) = -612 - 119 = -731 \][/tex]
[tex]\[ \left| \begin{pmatrix} 7 & -51 \\ 17 & -22 \end{pmatrix} \right| = (7 \cdot -22) - (-51 \cdot 17) = -154 + 867 = 713 \][/tex]
[tex]\[ \left| \begin{pmatrix} 12 & -13 \\ 7 & -51 \end{pmatrix} \right| = (12 \cdot -51) - (-13 \cdot 7) = -612 + 91 = -521 \][/tex]
From these calculations, the correct determinant matching [tex]\(\left|A_y\right|\)[/tex] is the one from:
[tex]\[ \left| \begin{pmatrix} 7 & -51 \\ 17 & -22 \end{pmatrix} \right| = 713 \][/tex]
So, [tex]\(\left|A_y\right|\)[/tex] is:
[tex]\[ 713 \][/tex]
The system of equations given is:
[tex]\[ \begin{cases} 12x - 13y = 7 \\ 17x - 22y = -51 \end{cases} \][/tex]
The coefficient matrix [tex]\(A\)[/tex] is:
[tex]\[ A = \begin{pmatrix} 12 & -13 \\ 17 & -22 \end{pmatrix} \][/tex]
The constants matrix is:
[tex]\[ \mathbf{b} = \begin{pmatrix} 7 \\ -51 \end{pmatrix} \][/tex]
To find [tex]\(\left|A_y\right|\)[/tex], we replace the second column of [tex]\(A\)[/tex] with [tex]\(\mathbf{b}\)[/tex]:
1. Start with possible replacements from the given options to construct the matrices.
[tex]\(\begin{pmatrix} 7 & -13 \\ -51 & -22 \end{pmatrix}\)[/tex]
2. Calculate the determinant:
[tex]\[ \left| \begin{pmatrix} 7 & -13 \\ -51 & -22 \end{pmatrix} \right| = (7 \cdot -22) - (-13 \cdot -51) = -154 - 663 = -817 \][/tex]
Following this result, let's analyze the determinants from the remaining options:
[tex]\[ \left| \begin{pmatrix} 12 & 7 \\ 17 & -51 \end{pmatrix} \right| = (12 \cdot -51) - (7 \cdot 17) = -612 - 119 = -731 \][/tex]
[tex]\[ \left| \begin{pmatrix} 7 & -51 \\ 17 & -22 \end{pmatrix} \right| = (7 \cdot -22) - (-51 \cdot 17) = -154 + 867 = 713 \][/tex]
[tex]\[ \left| \begin{pmatrix} 12 & -13 \\ 7 & -51 \end{pmatrix} \right| = (12 \cdot -51) - (-13 \cdot 7) = -612 + 91 = -521 \][/tex]
From these calculations, the correct determinant matching [tex]\(\left|A_y\right|\)[/tex] is the one from:
[tex]\[ \left| \begin{pmatrix} 7 & -51 \\ 17 & -22 \end{pmatrix} \right| = 713 \][/tex]
So, [tex]\(\left|A_y\right|\)[/tex] is:
[tex]\[ 713 \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.