Find the coefficient of x25 in (x2 + x3 + x4 + x5 + ...)8
; 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?
For the data x1 = -1, x2 = -3, x3 = -2, x4 = 1, x5 = 0, find ∑ (xi2).
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.
Consider the following linear transformation T: RS → R3 where T(X1, X2, X3, X4, X5) = (x1-X3+X4, 2X1+X2-X3+2x4, -2X1+3x3-3x4+x5) (a) Determine the standard matrix representation A of T(x).
Consider the following linear transformation T: R5 → R3 where T(X1, X2, X3, X4, X5) = (*1-X3+X4, 2X1+X2-X3+2x4, -2X1+3X3-3x4+x5) (a) Determine the standard matrix representation A of T(x). (b) Find a basis for the kernel of T(x). (c) Find a basis for the range of T(x). (d) Is T(x) one-to-one? Is T(x) onto? Explain. (e) Is T(x) invertible? Explain
9. Minimize x1 + x2 - X3, subject to 2x1 - 4x2 + x3 + x4 3xı + 5x2 + x3 +xs =2. Which of x1, x2, X3 should enter the basis, and which of x4, X5 should leave? Compute the new pair of basic variables, and find the cost at the new corner.
Express the following in the SIGMA notation: a. x1 +x2 +x3 +x4 +x5 b.x1 +2x2 +3x3 +4x4 +5x5
Question 19 Find the pivot in the tableau. X1 X2 X3 X4 X5 X6 Z 2 3 6 1 0 0 0 10 2 1 2 0 0 0 20 4 04 0 0 1 040 -2 4 -8 0 1 0 یہ نہ مانم plonu 1 oloor 1 in row 2, column 5 6 in row 1, column 3 O 3 in row 1, column 2 4 in row 3, column 1 Question 16 5 p Write the expression...
The coefficients respectively for X1, X2, X3, X4 and X5 are .01, .02, .03, .04 and .05. Compute the Z score. Analyze whether this firm will fail, or not and why. Explicate the meaning of the Xs.
12. Let X1,... , X5 be random variables with variance 4, and let Find Var(X1 X2+X3 + X4 +X5);