Homework Answers
(1 point) Consider the matrix -5 7 8-9 20 -30 8-3 -15 -19 9 -4 10-11 5-8 (a) On the matrix above,...
(1 point) Consider the matrix -5 7 8-9 20 -30 8-3 -15 -19 9 -4 10-11 5-8 (a) On the matrix above, perform the row operation R1 15 R1 . The new matrix is: (b) Using the matrix obtained in your answer for part (a) as the initial matrix, next perform the row operations () R3 R3 15R1, (iii) R4→R4+10R1. The new matrix is: (c) Using the matrix obtained in your answer for part (b) as the initial matrix, next...
(1 point) The matrix A = 1-6 1 8 k] 4 has two distinct real eigenvalues...
(1 point) The matrix A = 1-6 1 8 k] 4 has two distinct real eigenvalues if and only if k > 24.5
State the quadrant in which lies. sin(8) <0, cos(8) < 0 OII III OIV 8 If...
State the quadrant in which lies. sin(8) <0, cos(8) < 0 OII III OIV 8 If sin() and 8 is in the 1st quadrant, find the exact value for cos(8). 9 cos(8) - > Next Question State the quadrant in which lies. tan(8) > 0, csc(8) < 0 01 OII O III OIV
Exercise 1 Consider utility maximization problem: Kuhn Tucker Theorem max U (x1, x2) = x1+x2 21,22...
Exercise 1 Consider utility maximization problem: Kuhn Tucker Theorem max U (x1, x2) = x1+x2 21,22 subject to Tị 2 0, r2 > 0, p1x1+p2r2 < I, where p1, p2 and I are positive constants. Exercise 1 Consider utility maximization problem: Kuhn Tucker Theorem max U (x1, x2) = x1+x2 21,22 subject to Tị 2 0, r2 > 0, p1x1+p2r2 < I, where p1, p2 and I are positive constants.
4. Consider our standard LP: maxc.x subject to Ax <b and x > 0. Assume every...
4. Consider our standard LP: maxc.x subject to Ax <b and x > 0. Assume every entry of A is strictly positive and b > 0. Deduce that the LP has an optimal solution.
Prove each problem, prove by induction 3) Statementn-1 5 25(2m-1) forn2 1 4 Statement Suppose: bo1...
Prove each problem, prove by induction
3) Statementn-1 5 25(2m-1) forn2 1 4 Statement Suppose: bo1 . b,-2b-1 + 1 for t 1 en fort >
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
(1 point) If f(x) = { 6x, x39 8 x >9 Evaluate the integral 10 6."....
(1 point) If f(x) = { 6x, x39 8 x >9 Evaluate the integral 10 6.". f(x) dx |
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0)...
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0) 0 t> 8 Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)
Consider that V = R3 and W = {(a,b,c): a > 0} List 5 elements of...
Consider that V = R3 and W = {(a,b,c): a > 0} List 5 elements of W Is W a vector subspace? Justify
(1 point) Consider the matrix -5 7 8-9 20 -30 8-3 -15 -19 9 -4 10-11 5-8 (a) On the matrix above, perform the row operation R1 15 R1 . The new matrix is: (b) Using the matrix obtained in your answer for part (a) as the initial matrix, next perform the row operations () R3 R3 15R1, (iii) R4→R4+10R1. The new matrix is: (c) Using the matrix obtained in your answer for part (b) as the initial matrix, next...
(1 point) The matrix A = 1-6 1 8 k] 4 has two distinct real eigenvalues if and only if k > 24.5
State the quadrant in which lies. sin(8) <0, cos(8) < 0 OII III OIV 8 If sin() and 8 is in the 1st quadrant, find the exact value for cos(8). 9 cos(8) - > Next Question State the quadrant in which lies. tan(8) > 0, csc(8) < 0 01 OII O III OIV
Exercise 1 Consider utility maximization problem: Kuhn Tucker Theorem max U (x1, x2) = x1+x2 21,22 subject to Tị 2 0, r2 > 0, p1x1+p2r2 < I, where p1, p2 and I are positive constants. Exercise 1 Consider utility maximization problem: Kuhn Tucker Theorem max U (x1, x2) = x1+x2 21,22 subject to Tị 2 0, r2 > 0, p1x1+p2r2 < I, where p1, p2 and I are positive constants.
4. Consider our standard LP: maxc.x subject to Ax <b and x > 0. Assume every entry of A is strictly positive and b > 0. Deduce that the LP has an optimal solution.
Prove each problem, prove by induction
3) Statementn-1 5 25(2m-1) forn2 1 4 Statement Suppose: bo1 . b,-2b-1 + 1 for t 1 en fort >
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
(1 point) If f(x) = { 6x, x39 8 x >9 Evaluate the integral 10 6.". f(x) dx |
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0) 0 t> 8 Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)
Consider that V = R3 and W = {(a,b,c): a > 0} List 5 elements of W Is W a vector subspace? Justify
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