Question

Select the correct augmented matrices. Liam wants to buy a car and pay for it in three installments. The total cost of the car is $29,000. Two times the first installment is $1,000 more than the sum of the third installment and three times the second installment. Liam must pay 15% interest on the second and the third installments: the interest will amount to $2,100. If x, y, and z represent the first, second, and third installments, respectively, identify the augmented matrices that model Liam's situation.

Answer 1

To model Liam's situation, an augmented matrix can be used with variables representing the installments. The matrix will have three rows representing the given equations and one row for the total cost of the car. The first equation represents the total cost, the second equation represents the relationship between the installments, and the third equation represents the interest on the second and third installments.

Step-by-step explanation:

To model Liam's situation, we can create an augmented matrix using the variables x, y, and z to represent the first, second, and third installments, respectively. The total cost of the car is $29,000, so the first row of the augmented matrix would be [1, 1, 1, 29000].

According to the problem, two times the first installment is $1,000 more than the sum of the third installment and three times the second installment. This can be represented by the equation 2x = z + 3y + 1000. Converting this equation into the second row of the augmented matrix, we get [2, -3, -1, -1000].

Liam must pay 15% interest on the second and third installments, which amounts to $2,100. This can be represented by the equation 0.15y + 0.15z = 2100. Converting this equation into the third row of the augmented matrix, we get [0, 0.15, 0.15, 2100].