Question 1 • Advanced Algebra: Concepts and Connections
Which would be the next step in solving for matrix cap A ? cap A plus the 1 by 4 matrix, row 1, column 1, 3 column 2, negative 4 column 3, negative 11 column 4, 24 is equal to the 1 by 4 matrix, row 1, column 1, 16 column 2, negative 5 column 3, 0 column 4, negative 9
Answer
A
cap A is equal to the 1 by 4 matrix, row 1, column 1, 16 column 2, negative 5 column 3, 0 column 4, negative 9 minus the 1 by 4 matrix, row 1, column 1, 3 column 2, negative 4 column 3, negative 11 column 4, 24
B
cap A is equal to the 1 by 4 matrix, row 1, column 1, 16 column 2, negative 5 column 3, 0 column 4, negative 9 times the 1 by 4 matrix, row 1, column 1, 3 column 2, negative 4 column 3, negative 11 column 4, 24
C
cap A is equal to the 1 by 4 matrix, row 1, column 1, 16 column 2, negative 5 column 3, 0 column 4, negative 9 divided by the 1 by 4 matrix, row 1, column 1, 3 column 2, negative 4 column 3, negative 11 column 4, 24
D
cap A is equal to the 1 by 4 matrix, row 1, column 1, 16 column 2, negative 5 column 3, 0 column 4, negative 9 plus the 1 by 4 matrix, row 1, column 1, 3 column 2, negative 4 column 3, negative 11 column 4, 24
Explanation
To isolate matrix A in A + X = Y, subtract X from both sides. This gives A = Y − X, where Y is the matrix with entries 16, −5, 0, −9 and X is the matrix with entries 3, −4, −11, 24. So the next step is the subtraction shown in choice C.
AI-written and checked against the verified answer.