Question 24 • Advanced Algebra: Concepts and Connections
Given: cap A is equal to the 2 by 2 matrix, row 1, column 1, negative 3 column 2, negative 4 row 2, column 1, 1 column 2, 0 , cap b is equal to the 2 by 2 matrix, row 1, column 1, negative 7 column 2, negative 9 row 2, column 1, 4 column 2, negative 1 , and cap c is equal to the 2 by 2 matrix, row 1, column 1, negative 42 column 2, negative 20 row 2, column 1, 5 column 2, 4 What is the value of cap x in the matrix equation cap A cap x plus cap b is equal to cap c ?
Answer
A
cap x is equal to the 2 by 2 matrix row 1, 9 3 row 2, 5 point 5 5
B
cap x is equal to the 2 by 2 matrix, row 1, column 1, 101 column 2, 13 row 2, column 1, negative 35 column 2, negative 11
C
cap x is equal to the 2 by 2 matrix, row 1, column 1, 1 column 2, 5 row 2, column 1, 8 column 2, negative 1
D
cap x is equal to the 2 by 2 matrix, row 1, column 1, 2 point 7 5 column 2, negative 26 point 2 5 row 2, column 1, 1 point 7 5 column 2, negative 2 point 7 5
Explanation
Rearrange the equation to get AX = C − B. Subtracting gives C − B = [[−35, −11], [1, 5]]. For each column, the second row of AX equals the first row of X, so those entries are 1 and 5; using the first row, −3x − 4y, gives the remaining entries 8 and −1. Thus X = [[1, 5], [8, −1]], choice C.
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