4. Let B = {x6 + 3, x5 + x3 + 1, x4 + x3, x3 + x2} C Pg, where Pg is the polynomials of degree < 8. (a) (2 marks) Explain why B is a linearly independent subset of Pg. (b) (2 marks) Extend B to a basis of Pg by adding only polynomials from the standard basis of Pg.
Question 1,2,3,4 11) Maximize z» x 1 + 2x2 subject to: x1+ x2 s20 3x1+ 2x2 40 2x13x2 60 x1z0 x20 Use th perfor x1 A) Find the pivot in the tableau. 1 x2 x3 x4 x5 2 3 1 4 02 0 9 6 0 2 1 5 0 3 B) Find the plvot in the tableau. C) 1 2 3 10 0 ol 4 1 4 4 0 1 0 0 12 1 2 2 oo1 06 1...
X1, X2, X3, X4,X5,X6,X7,X8 are independent identically distributed random variables. Their common distribution is normal with mean 0 and variance 4. Let W = X12+ X22 + X32 + X42+X52+X62+X72+X82 . Calculate Pr(W > 2)
c. Now write the general solution in parametric form. x = X11 X2 X3 XA X5 = P + (vectors multiplied by free variables) (Fill in the particular vector p, then factor out any remaining free variables from your expression above.) (4 points) particular 1 X2 X3 II II X4 + X2 X5 + 0 0 LX6 0 X₂ X₂ X₃ X4 Xg X6 1 2 3 0 5 6 d. Write a vector equation equivalent to the reduced system:...
For the data x1 = -1, x2 = -3, x3 = -2, x4 = 1, x5 = 0, find ∑ (xi2).
; Let at be a linear transformation as follows : T{x1,x2,x3,x4,x5} = {{x1-x3+2x2x5},{x2-x3+2x5},{x1+x2-2x3+x4+2x5},{2x2-2x3+x4+2x5}] a.) find the standard matrix representation A of T b.) find the basis of Col(A) c.) find a basis of Null(A) d.) is T 1-1? Is T onto?
3. Description of each X and data for 27 franchise stores are given below The data (X1, X2, X3, X4, X5, X6) are for each franchise store. X1 annual net sales/$1000 X2 number sq. ft/1000 X3 - inventory I$1000 X4- amount spent on advertising /$1000 X5 size of sales district/1000 families X6 number of competing stores in distric X1 X2 X3 X4 X5 X6 231 3 294 8.2 8.2 11 156 2.2 232 6.9 4.1 12 10 0.5 149 3...
b. Given the following tableau find an alternative basic feasible optimal solution. (10 pts) 2 X, X2 X3 X4 X5 X6 RHS 2 1 0 0 0 0 2 3 4 X 0 1 0 2 -1 -1 1 2 X, 0 0 -2 2 3 2
Question 9 Find the value(s) of the function on the given feasible region. Find the maximum and minimum of z = 8x + 8y. K0,5) (5/2,5) (0,4) (6,0) (10,0) 56,32 80,32 -32,-56 48,40 Question 11 Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. In V10192 In 10+ 3 Int+2 in v 01/ in In 90t + 2 in v Jin In 10+ 3 Int + In v In 10 +...
Problem No-3 Implement the following two-level function using multi-level NOR gates: f(x1,X2.X3,X4,X5,X6,x7)=X1X«X5+X\X4X¢+> kaX4X6+X2X3X7 [9] Assume that logic gates have a maximum fan in of 2 and the input variables are available in uncomplemented form only (The number of gates required is shown in parenthesis).