Connect with a global community of experts on IDNLearn.com. Join our community to access reliable and comprehensive responses to your questions from experienced professionals.
Sagot :
To solve the given problem, we need to determine the value of [tex]\(\left|A_y\right|\)[/tex].
Given the matrix equation:
[tex]\[ \left[\begin{array}{ll}12 & -13 \\ 17 & -22\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}7 \\ -51\end{array}\right] \][/tex]
We need to identify the matrix whose determinant is requested. The matrix associated with the notation [tex]\(\left|A_y\right|\)[/tex] corresponds to the column of constants replacing the [tex]\(y\)[/tex]-column of the original matrix. As stated in the problem, we need [tex]\(\left|A_y\right|\)[/tex].
Replacing the [tex]\(y\)[/tex]-column ([tex]\([-13, -22]\)[/tex]) with the constants vector ([tex]\([7, -51]\)[/tex]), we get the augmented matrix:
[tex]\[ \left[\begin{array}{cc} 12 & 7 \\ 17 & -51 \end{array}\right] \][/tex]
However, the task is to identify the correct matrix from the provided ones. Among these matrices, the matching structure, where the [tex]\(y\)[/tex]-column is replaced by the constants is:
[tex]\[ \left[\begin{array}{cc} 7 & -51 \\ 17 & -22 \end{array}\right]. \][/tex]
So, our focus is on the matrix:
[tex]\[ \left[\begin{array}{cc} 7 & -51 \\ 17 & -22 \end{array}\right] \][/tex]
To determine [tex]\(\left|A_y\right|\)[/tex], we find the determinant of this matrix. The determinant for a 2x2 matrix [tex]\(\left[\begin{array}{cc} a & b \\ c & d \end{array}\right]\)[/tex] is given by:
[tex]\[ \left| \begin{array}{cc} 7 & -51 \\ 17 & -22 \end{array}\right| = 7 \cdot (-22) - (-51) \cdot 17 = -154 + 867 = 713. \][/tex]
Thus, the determinant [tex]\(\left|A_y\right|\)[/tex] is:
[tex]\[ \boxed{713}. \][/tex]
Given the matrix equation:
[tex]\[ \left[\begin{array}{ll}12 & -13 \\ 17 & -22\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}7 \\ -51\end{array}\right] \][/tex]
We need to identify the matrix whose determinant is requested. The matrix associated with the notation [tex]\(\left|A_y\right|\)[/tex] corresponds to the column of constants replacing the [tex]\(y\)[/tex]-column of the original matrix. As stated in the problem, we need [tex]\(\left|A_y\right|\)[/tex].
Replacing the [tex]\(y\)[/tex]-column ([tex]\([-13, -22]\)[/tex]) with the constants vector ([tex]\([7, -51]\)[/tex]), we get the augmented matrix:
[tex]\[ \left[\begin{array}{cc} 12 & 7 \\ 17 & -51 \end{array}\right] \][/tex]
However, the task is to identify the correct matrix from the provided ones. Among these matrices, the matching structure, where the [tex]\(y\)[/tex]-column is replaced by the constants is:
[tex]\[ \left[\begin{array}{cc} 7 & -51 \\ 17 & -22 \end{array}\right]. \][/tex]
So, our focus is on the matrix:
[tex]\[ \left[\begin{array}{cc} 7 & -51 \\ 17 & -22 \end{array}\right] \][/tex]
To determine [tex]\(\left|A_y\right|\)[/tex], we find the determinant of this matrix. The determinant for a 2x2 matrix [tex]\(\left[\begin{array}{cc} a & b \\ c & d \end{array}\right]\)[/tex] is given by:
[tex]\[ \left| \begin{array}{cc} 7 & -51 \\ 17 & -22 \end{array}\right| = 7 \cdot (-22) - (-51) \cdot 17 = -154 + 867 = 713. \][/tex]
Thus, the determinant [tex]\(\left|A_y\right|\)[/tex] is:
[tex]\[ \boxed{713}. \][/tex]
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.