Question 8 - Week 5 Practice

Question 8

00:00Est. 1 min

Marks:+1.000.00

Passage

Shivani, Sruthi and Smriti enjoyed shopping on a Sunday. Shivani bought 2 shirts, a T-shirt and 2 pants, whereas Sruthi bought a T-shirt and a pant and Smriti bought 2 shirts and a pant. They paid Rs. 600, Rs. 400 and Rs. 300 respectively. Suppose

x_1

is the price of a shirt,

x_2

is the price of a T-shirt and

x_3

is the price of a pant. Then the above information forms a system of linear equations. If

Ax=b

is the matrix representation of the above system, where

x=[x_1,x_2,x_3]^T

is the vector that represents the price of a shirt, T-shirt and pant respectively, answer the given subquestions.

Question

Consider the set

S

of solutions of the system

Ax=0

, where

A

is as given. Clearly,

S

is a vector space with respect to usual addition and scalar multiplication. What is the dimension of

S

Comprehension

Easy Difficulty

16 July 2023

Your answer