2. Three equal charges of 2.0 μ Coul are located on the corners of a square, 3.0 mm on a side. What is the magnitude of the electric field at the fourth corner? What is its direction?

9. The Medequip Company produces precision medical diagnostic equipment at two factories. Three medical centers have placed orders for this month's production output. The table below shows what the cost would be for shipping each unit from each factory to each of these customers. Also shown are the number of units that will be produced at each factory and the number of units ordered by each customer. A decision now needs to be made about the shipping plan for how many units to ship from each factory to each customer.

2.Describe the span of the given vectors geometrically and algebraically. a.The set of all linear combinations of u, v, and w is a line through the origin with u as a direction vector. b.The set of all linear combinations of u, v, and w is a line through the origin with v as a direction vector. C.The set of all linear combinations of u, v, and w is a plane through the origin containing only u as a direction vector. d.The set of all linear combinations of u, v, and w span R3. е.The set of all linear combinations of u, v, and w is a plane through the origin containing u and v as direction vectors.

7. The folium of Descartes is a curve defined by the equation r³ + y³ – 3xy = 0 and shown in the diagram below. Determine the exact coordinates of the point P on the curve where the tangent line is parallel to the y-axis. (6 marks)

3. Consider the following set of vectors. Let v1, V2, V3, and v4 be (column) vectors in Rª and let A be the 4 X4 matrix vị V2 V3 V4with these vectors as its columns. Then v1, V2, V3, and v4 are linearly dependent if and only if the homogeneous linear system with augmented matrix [A|0] has a nontrivial solution. Consider the following equation. Solve for and the parameter: (If only the trivial solution exists, enter the trivial solution If a nontrivial solution exists, state it or state the general solution in terms of

26.)use the graphs of x= f(t) and y=g(t) to sketch the parametric curve x= f(t) y=g(t) indicate with arrows the direction in which the curve is traced as t increases

Let W1 be the set: Determine if W1 is a basis for R° and check the correct answer(s) below. O A. Wi is a basis. OB. W, is not a basis because it is linearly dependent. OC. W, is not a basis because it does not span R. Let W2 be the set: \left[\begin{array}{ccccc} -2 & & & & 6 & \\ 3 & & & & & \\ 0 & & & & 5 & \end{array}\right] Determine if W2 is a basis for R° and check the correct answer(s) below. W2 is a basis. W2 is not a basis because it does not span R.

5. Four neighbors, each with a vegetable garden, agree to share their produce. One will grow beans (B), one will grow lettuce (L), one will grow tomatoes (T), and one will grow zucchini (Z).Table 2.9 shows what fraction of each crop each neighbor will receive. What prices should the neighbors charge for their crops if each person is to break even and the lowest-priced crop has a value of $50.00?

3. (5 points) Suppose A is a 4x3 matrix and B is a 3x4 matrix. Explain why the matrixproduct AB cannot possibly be the identity matrix I4. Hint: you may want to consider the RREF of A and/or B.

a) The contour diagram of the function f(x, y) is shown below. At the point corresponding to (2,1) is the function increasingdecreasing withorrespect to x? At the point corresponding to (4, 2) is the function increasingrespect to y?decreasing withor (c) Suppose a bug is walking along the graph of f(x, y). If the bug walks in a straight line from the point corresponding to (1,3) to the point corresponding to (4, 1), is the bug walking uphill or downhill?

1. Determine if the vector b is in the span of the columns of the matrix A. Circle the correct answer. a. The vector b is in the span of the columns of the matrix A. b. The vector b is not in the span of the columns of the matrix A.