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Let A = 3i + 4j and B = 5i ¡ 6j. (i) Find A + B, A ¡ B, 2A + 3B, and C such that A + B + C = 0: (ii) Find A, the length of A and the angle it makes with the x-axis.
Given the vectors: A = 3i - 4j, B = 5i +6j & C= -2i - 2j. Find the following: a) 2(A-C) + 3 B b) 3B -4C +A . A car traveling in a straight line with an initial velocity of 10 m/s accelerates at a rate of 4 m/sto a velocity of 30 m/s. a) How much time does it take for the car to reach the velocity of 30 m/s? b) What is the distance covered by...
Given two vector A=5i+4j and B=3i-4j A: Draw each vector in a vector diagram. B: Find the magnitude of each vector. C: Express vector c=3A-1/3B in terms of unit vectors D: Calculate the magnitude and direction of vector C
#1,5,9 and #13,17,21,25 please.
In Exercises 1-12, graph each complex number in the complex plane 3. -2 4i 2 2. 3 5i 7.-3i 8.-5i 6. 7 47 19 7 15 2 11 2 12. 10 10 each complex number in polar form 15. 1 V3i 14. 2 + 2i 16. -3- V3i 3. 1-i 20. -V3+i 18. V5_V5İ 19. V3-3i 17-44i 24. -8-8V3i 22. 2 + Oi 2 23, 2v3-2i 21. 3 +0i V3 1 1 V3 28·16+161 26, 1...
Graph and determine the magnitudes of the following complex numbers. 1. 3+5i 2. -1 + 3i 3. 2-4 Write each of the following complex numbers in trigonometric form. 17.-3-i 23. 2-2i Write each of the complex numbers in standard form. 570 COS 6 29. 51 +isin 6 30. cos - +isin 3 costising
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A using the cofactor expansion technique along (a) row 1 and (b) column 3. (ii) In trying to find the inverse of A, applying four elementary row operations reduces the aug- mented matrix [A1] to -2 0 0 0 0 -2 2 1 3 0 1 0 1 0 -2 Continue with row reductions to obtain the augmented matrix [1|A-') and thus give the in-...
Consider the following reward matrix for a two-person zero-sum game: 9 0 6 3 2 4 3 1 5 (a) Find optimal strategies for both the row and column players. (b) What is the value of the game to the column player?. (c) Who is favoured by the game?
1. Consider the system 2(t)--3i(t) +z2(t) +3() (a) (i) Find the linearised system at the equilibrium point (0, 0). (ii) What type of equilibrium point is (0,0)? (State your reasons fully.) (ii) Sketch the phase portrait for the linearised system near (0,0). (b) Repeat part (a) for the equilibrium point at (1,0). (c) (i) Are there any other equilibria? (ii) Read the Grobman-Hartman theorem and confirm that it applies to the above equilibria.
1. Consider the system 2(t)--3i(t) +z2(t) +3()...
Find R and angle. Z1 =8+3i, Z2 =2+3i,
Z3 =9-((2)^1/2 )i.
(vi) z = TEM (vii) 2 = 22 + 231
Find the following: z2+9 e) lim 23į 2-3i z2+i f) lim 2-i 24-1 Write given numbers in the polar form reio: 3 a) (cos 29 + i sin 27)