Question

Vinayak runs a bakery shop. He sells three items: Sandwiches (₹x per unit), Fruit juices (₹y per unit) and Cookies (₹z per unit). The sales revenue over three days are 37, 26 and 37 respectively. The entire information is given below as matrix equation.

Consider A = `((2,3,1),(1,2,3),(3,1,1))` and |A| = 17. Find the price per unit for each item using matrix method.

Answer 1

Using matrix Method:

AX = B

X = A⁻¹ × B

X = `"adj" (A × B)/|A|` 

|A| = 17

A = `((2,3,1),(1,2,3),(3,1,1))`

adj A = `((−1,−2,7),(8, −1,−5),(−5,7,1))`

A⁻¹ = `1/17 ((−1,−2,7),(8,−1,−5),(−5,7,1))`

`((x),(y),(z)) = ((10),(5),(2))`

• Price of one Sandwich (x) = ₹ 10 
• Price of one Fruit Juice (y) = ₹ 5
• Price of one Cookie (z) = ₹ 2