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1)  If 1900 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. 2) A rancher wants to fence in an area of 2500000 square feet in a rectangular field and then divide it in half with a fence down …

1) If 1900 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.2) A rancher wants to fence in an area of 2500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use? Read More »

Determine whether b is in the column space of A. If it is, then write b as a linear combination of the column vectors of A. (Use v1, v2, and v3, respectively, for the three columns. If not possible, enter IMPOSSIBLE.) A = [(1,3,0);(-1,1,0);(2,0,1)] b= [(2,3,-4)] EXPERT ANSWER

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5. Suppose that x1 =3, x2 =0, x3 =−1, x4 =5 is a solution of a nonhomogeneous linear system Ax=b and that the solution set of the homogeneous system Ax=0 is given by the formulas x1 =5r −2s, x2 =s, x3 =s+t, x4 =t (a) Find a vector form of the general solution of Ax=0. …

5. Suppose that x1 =3, x2 =0, x3 =−1, x4 =5 is a solution of a nonhomogeneous linear system Ax=b and that the solution set of the homogeneous system Ax=0 is given by the formulasx1 =5r −2s, x2 =s, x3 =s+t, x4 =t Read More »

EXPERT ANSWER

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Prove by induction that 11! + 22! + 33! +… + nn! = (n+1)! – 1 for positive integer n. EXPERT ANSWER here bold N is stand for Natural number. i.e positive natural number

Prove by mathematical induction for n ≥ 1 1(1!) + 2(2!) + 3(3!) + … + n(n!) = (n+1)! – 1 EXPERT ANSWER

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