Lab 6: Matrices T2.1-1 For the matrix B, nd the array that results from the operation [B; B']. Use MATLAB to determine what number is in row 5, column 3 of the result. 2 4 10 13 16 3 7 18 B = 8 4 925 3 12 15 17 T2.1-2 For the same matrix B, use MATLAB to (a) nd the lar gest and smallest elements in B and their indices and (b) sort each column in B to create a new matrix C. T2.3-1 Given the matrices A = [ 21 27 -7 -3 B = -18 8 9 4 nd (a) their array product, (b) their array right division ( A divided by B), and (c) B raised to the third power element by element. T2.4-1 Use MATLAB to compute the dot product of the following vectors: u = 6i - 8j + 3k w = 5i + 3j - 4k T2.4-2 Use MATLAB to show that 74 35 80 1 8 -3 2 = 11 -12 7 6 59 68 94 5. Type this matrix in MATLAB and use MATLAB to carry out the following instructions. 3 7 -4 12 -5 9 10 2 A = 6 13 8 11 15 5 4 1 6. a. Create a vector v consisting of the elements in the second column of A. b. Create a vector w consisting of the elements in the second row of A. Type this matrix in MATLAB and use MATLAB to carry out the following instructions. A || 3 7 -5 9 -4 12 10 2 6 13 8 11 15 5 4 1 a. Create a 4 × 3 array B consisting of all elements in the second through fourth columns of A. b. Create a 3 × 4 array C consisting of all elements in the second through fourth rows of A. c. Create a 2 × 3 array D consisting of all elements in the rst two rows and the last three columns of A. 8. Given the matrix 3 7 -4 12 -5 9 10 2 A = 6 13 8 11 15 5 4 1 a. Find the maximum and minimum values in each column. b. Find the maximum and minimum values in each row. 10. Consider the following arrays. A || 1 4 2 2 4 100 B = ln(A) 7 9 7 3 TT 42 Write MATLAB expressions to do the following. a. Select just the second row of B. b. Evaluate the sum of the second row of B. c. Multiply the second column of B and the rst column of A element by element. d. Evaluate the maximum value in the vector resulting from element-by- element multiplication of the second column of B with the rst column of A. 14.* The mechanical work W done in using a force F to push a block through a distance D is W = FD. The following table gives data on the amount of force used to push a block through the given distance over ve segments of a certain path. The force varies because of the differing friction proper- ties of the surface. Path segment 1 2 3 4 5 Force (N) Distance (m) 400 550 700 500 3 0.5 0.75 1.5 600 5 Use MATLAB to nd (a) the work done on each segment of the path and (b) the total work done over the entire path.