You have been asked to explore a range of engineering problems that will require you to...

 

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You have been asked to explore a range of engineering problems that will require you to solve problems involving matrices, determinants and complex numbers. 1. Use your given matrices to solve your given problems. Give reasons if the procedure is not possible. A = (246) B = C = = ( D= (-1 2) 1 0 2 E=3 11 -1 2 3/ = 5) G= 2 3 F-(9) -() -(1) 2 3 2 4 3 1 1 I 1 = (24) J= 2 0 1 -1 2 4 (a) X + Y (b) X. Z (c) Z. X (d) 3X (e) 3X - Y 2. Calculate the determinant of each of your given 2 x 2 and 3 x3 matrices. 3. Solve your given pair of simultaneous equations (with two variables) using matrix and determinant methods. Bx-2y=-5 C 3x + y = 13 A 2x + 3y = 18 D 4x-y=8 E 6x-3y = 6 F 5x-4y=-1 4. Solve your set of simultaneous equations (with three variables) using matrix and determinant methods. A 2a-2b+ 2c=2 B-a-b+c=3 C 3a - b + 2c=3 Da+b+2c = 11 E 3a + b - 2c=-9 F 2a+3b+c=8 You have been asked to explore a range of engineering problems that will require you to solve problems involving matrices, determinants and complex numbers. 1. Use your given matrices to solve your given problems. Give reasons if the procedure is not possible. A = (246) B = C = = ( D= (-1 2) 1 0 2 E=3 11 -1 2 3/ = 5) G= 2 3 F-(9) -() -(1) 2 3 2 4 3 1 1 I 1 = (24) J= 2 0 1 -1 2 4 (a) X + Y (b) X. Z (c) Z. X (d) 3X (e) 3X - Y 2. Calculate the determinant of each of your given 2 x 2 and 3 x3 matrices. 3. Solve your given pair of simultaneous equations (with two variables) using matrix and determinant methods. Bx-2y=-5 C 3x + y = 13 A 2x + 3y = 18 D 4x-y=8 E 6x-3y = 6 F 5x-4y=-1 4. Solve your set of simultaneous equations (with three variables) using matrix and determinant methods. A 2a-2b+ 2c=2 B-a-b+c=3 C 3a - b + 2c=3 Da+b+2c = 11 E 3a + b - 2c=-9 F 2a+3b+c=8