Question 7 • Advanced Algebra: Concepts and Connections
Which determinants can be used to solve for x and y in the given system of linear equations? negative 3 x plus 2 y is equal to negative 9 4 x minus 15 y is equal to negative 25
Answer
A
the 1 by 1 row matrix cap A is equal to the 2 by 2 matrix, row 1, column 1, negative 3 column 2, 2 row 2, column 1, 4 column 2, negative 15 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 3 column 2, negative 9 row 2, column 1, 4 column 2, negative 25 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 9 column 2, 2 row 2, column 1, negative 25 column 2, negative 15
B
the 1 by 1 row matrix cap A is equal to the 2 by 2 matrix, row 1, column 1, negative 3 column 2, 2 row 2, column 1, 4 column 2, negative 15 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 9 column 2, 2 row 2, column 1, negative 25 column 2, negative 15 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 3 column 2, negative 9 row 2, column 1, 4 column 2, negative 25
C
the 1 by 1 row matrix cap A is equal to the 2 by 1 column matrix row 1 negative 9 row 2 negative 25 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 9 column 2, 2 row 2, column 1, negative 25 column 2, negative 15 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 3 column 2, negative 9 row 2, column 1, 4 column 2, negative 25
D
the 1 by 1 row matrix cap A is equal to the 2 by 1 column matrix row 1 negative 9 row 2 negative 25 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 3 column 2, negative 9 row 2, column 1, 4 column 2, negative 25 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 9 column 2, 2 row 2, column 1, negative 25 column 2, negative 15