answer:The product of the two matrices is: left( begin{array}{cccc} (-1)(-3) + (-2)(-3) + (-1)(1) & (-1)(-2) + (-2)(0) + (-1)(-3) & (-1)(3) + (-2)(-1) + (-1)(-1) & (-1)(-2) + (-2)(2) + (-1)(3) (-2)(-3) + 2(-3) + 1(1) & (-2)(-2) + 2(0) + 1(-3) & (-2)(3) + 2(-1) + 1(-1) & (-2)(-2) + 2(2) + 1(3) (1)(-3) + 0(-3) + 1(1) & (1)(-2) + 0(0) + 1(-3) & (1)(3) + 0(-1) + 1(-1) & (1)(-2) + 0(-2) + 1(3) end{array} right) Simplifying each element gives: left( begin{array}{cccc} 9 & 12 & 4 & -3 -4 & 11 & -4 & 3 -3 & 0 & 6 & 3 end{array} right)

answer:To find the indefinite integral of the given function, displaystyle int left (4 x^2 + x + 3right ) dx we will apply the sum rule, constant multiplication rule, and the power rule for integration. Using the sum rule, we can write the integral as the sum of individual integrals: {eq}begin{align*} int left (4 x^2 + x + 3right ) dx &= int 4x^2, dx + int x, dx + int 3, dx end{align*} Next, apply the constant multiplication rule: {eq}begin{align*} &= 4 int x^2, dx + int x, dx + 3 int dx end{align*} Now, use the power rule for each integral: {eq}begin{align*} &= 4 left ( frac{x^3}{3} right ) + left ( frac{x^2}{2} right ) + 3x + C &= frac{4x^3}{3} + frac{x^2}{2} + 3x + C end{align*} Thus, the indefinite integral is: {eq}boxed{dfrac{4x^3}{3} + dfrac{x^2}{2} + 3x + C} {/eq}

answer:Montresor's requirements for revenge were twofold: 1. The revenge must be complete and satisfying, leaving no doubt in Fortunato's mind that he had been wronged. 2. Montresor must remain anonymous, so that Fortunato would never know who had taken revenge on him. Montresor followed through with these requirements by carefully planning and executing his plan. He lured Fortunato to his home under the pretense of tasting a rare Amontillado, then led him to the catacombs beneath his house. Once there, he chained Fortunato to the wall and began to brick him up alive. As he worked, Montresor taunted Fortunato, reminding him of the insults he had suffered and reveling in his impending doom. When the wall was finally complete, Montresor left Fortunato to die, alone and in darkness.

answer:When a variable is restricted from both sides, such as x_1 in your problem, you can split the inequality into two separate inequalities. For 1 leq x_1 leq 4, you would write: x_1 geq 1 x_1 leq 4 Now, to convert the equation 5x_1 - 2x_3 = 6 into an inequality, you can rewrite it as: 5x_1 - 2x_3 - 6 leq 0 -(5x_1 - 2x_3 - 6) leq 0 -5x_1 + 2x_3 + 6 leq 0 The standard form of a linear programming problem involves inequalities of the form h(mathbf{x}) leq 0, where mathbf{x} = (x_1, x_2, x_3)^top. The revised constraints in standard form are: Maximize: -x_1 + 2x_2 - 3x_3 Subject to: 5x_1 - 6x_2 - 2x_3 leq 2 -5x_1 + 2x_3 + 6 leq 0 x_1 - 3x_2 + 5x_3 geq -3 x_1 geq 1 x_1 leq 4 x_3 leq 3 To find the optimal solution, you can solve for the vertices of the feasible region by intersecting the constraints. Since x_1 should be maximized and x_2 minimized, you should focus on the intersection points involving x_1 and x_3, as they directly impact the objective function. The intersection points of 27x_3 - 15x_2 geq -21 and 6 - 4x - 2y = 2 will give you one such vertex. From there, you can compare the objective function values at each vertex to determine the maximum value.