918 CHAPTER 9 Systems and Matrices 88. Roof Trusses (Refer to Exercise 87.) Use the following system of equations to determine the forces or weights W1 and W2 exerted on each rafter for the truss shown in the figure. W1 + 22W2 = 300 23W1 - 22W2 = 0 To solve a determinant equation such as 2 6 4 -2 x2 = 2, expand the determinant to obtain 6x - 1-22142 = 2. Then solve to obtain the solution set 5-16. Use this method to solve each equation. 95. 2 5 -3 x 22 = 6 96. 2 -0.5 x 2 x2 = 0 97. 2 x x 3 x2 = 4 98. 2 2x 11 x x2 = 6 99. 3 -2 -1 5 0 3 -2 1 x 03 = 3 100. 3 4 2 -3 3 0 x 0 1 -13 = 5 101. 3 5 0 4 3x 2 -1 -3 -1 x3 = -7 102. 3 2x 0 3 1 4 0 -1 x 23 = x 103. 3 x 2 x 0 -3 0 -1 x 73 = 12 104. Concept Check Write the sign array representing 1-12i+j for each element of a 4 * 4 matrix. 150 lb 308 458 W2 W1 Area of a Triangle A triangle with vertices at 1x1, y12, 1x2, y22, and 1x3, y32, as shown in the figure, has area equal to the absolute value of D, where D= 1 2 3 x1 x2 x3 y1 y2 y3 1 1 13 . Find the area of each triangle having vertices at P, Q, and R. 89. P10, 02, Q10, 22, R11, 42 90. P10, 12, Q12, 02, R11, 52 91. P12, 52, Q1-1, 32, R14, 02 92. P12, -22, Q10, 02, R1-3, -42 93. Area of a Triangle Find the area of a triangular lot whose vertices have the following coordinates in feet. Round the answer to the nearest tenth of a foot. 1101.3, 52.72, 1117.2, 253.92, and 1313.1, 301.62 (Data from Al-Khafaji, A., and J. Tooley, Numerical Methods in Engineering Practice, Holt, Rinehart, and Winston.) 94. Let A = £ a11 a21 a31 a12 a22 a32 a13 a23 a33§. Find A by expansion about row 3 of the matrix. Show that the result is really equal to A as given in the definition of the determinant of a 3 * 3 matrix at the beginning of this section. x y 0 P(x1, y1) R(x3, y3) Q(x2, y2)
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