ECON 1003 - Graded Tutorial 3 (5%) (Due March 23rd 2017) Question 1 a. Given supply function, Q s (p) = ap2 + bp + c, for the constants a, b and c. Also, that the quantity supply is 2 kgs when p is $1, it is 8 kgs when p is $2 and 16 kgs when p is $3. Formulate a system of three linear equations in the variables a, b and c. b. Write the system below in the form Ax = b, where A is a 3x3 matrix of coefficients, x is a 3x1 vector of variables and b is a 3x1 vector of constant terms. y 2x 1 + 6z = 0 2z + 4x = 18 6z + x = y + 5z + 3 Question 2 Find the determinant of the following matrices: 1 2 1 a. = (3 3 6) 7 2 4 4 2 1 b. = (7 9 1 ) 3 0 8 Question 3 4 0 a. Calculate, if possible, the inverse of matrix = (0 1 3 0 4 0 8 = (0 1 6). 2 0 4 5 6) and 4 Question 4 3 2 1 2 a. Given = ( 0 4 ) and = (0 1) 1 1 1 1 i. Find a matrix such that = . ii. Find a matrix such that + + = . b. 3 2 i. For which value(s) of x is the = |x x | singular? 4 x 2 1 ii. For = ( show that any scalar , show that the value of ), 5 6 || = 2 ||. 1