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11 O-I-1 6 2 3 4. LetA=(1 2 3 4) 5 67 8 15 in Nul)? Explain. a. Is 14 -23 in Nul(A)? Explain. b. Is in Col(A)? Explain. c. Is 10 5. Let A =(2 2 a. Find the characteristic polynomial of A.
Mathematical theory of games 11. (15%) Solve each game. 0 1 -2 (a) 3 2 -3 0 1-2 (b) 2 0 1 1 -2 1 4-1 5 4 -1 51 (e) 1 5 14 5 14-1 22 2 2/ 11. (15%) Solve each game. 0 1 -2 (a) 3 2 -3 0 1-2 (b) 2 0 1 1 -2 1 4-1 5 4 -1 51 (e) 1 5 14 5 14-1 22 2 2/
45 points) Consider the following vectors in R3 2 0 0 2 2 Vi = 1 ;02 31; V3 = 11:04 = -1 ; Us = 4 2 2 3 (c) Find a basis of R3 among V1, V2, V3, V4, V5, and call it basis V. (d) Is vs Espan{V1, V2, 03, 04}? Explain. (e) Find the coordinates of us with respect to the basis V.
2 3 S1 0 1 0 114 4 13 1 0 15 7 2 4 1 14 3|15 12 8 4 5 6 7 8 9 10 11 12 13 14 15 1 2 15 11 8 3 10 6 12 5 9 0 7 4 14 2 13 1 10 6 12 11 9 5 3 8 8 13 6 2 11 15 12 9 7 3 10 5 0 2 4 9 1 7 5 11 0 6...
15 points) Consider the following vectors in R3 0 0 2 V1 = 1 ; V2 = 3 ; V3 = 1] ; V4 = -1;V5 = 4 1 2 3 = a) Are V1, V2, V3, V4, V5 linearly independent? Explain. b) Let H (V1, V2, V3, V4, V5) be a 3 x 5 matrix, find (i) a basis of N(H) (ii) a basis of R(H) (iii) a basis of C(H) (iv) the rank of H (v) the nullity...
T25-1] 4 1and A0 1-1. Is u in the subset 4 14. Letu-1 0」 of R3 spanned by the columns of A? Why or why not?
Consider T:R4 → R3 with 1 [T) 3 2 -4-1 0 0 5 7 8 10 4 3 -20 -6 1 0 0 5 om Find a basis for image(T). What is dim(image(T))? Convert image(T) to relation form.
5002 } 0 2 100Le Ⓡ 100 javo Figure 3: For Questions 14 and 15 4. For the circuit shown in figure 3, what value of XL will ensute most power transfer if it is restricted to multiples of +j6? (a)-j182 (b)-j122 (c) j182 (d) j122 (e) None of the above
If A=[(1, 2,1) (2, 0, 0) (0, 5, 0)] A: R3->R3 1) Find the row reduced echelon form of A 2) Find the image of A 3) Find a nonzero vector in ker(A)
Pivot the following matrix, -3 9 15 -6 3 5 2 2 -4 -1 -4 -1 about the entry a11. (A) 1 -3 -5 2 0 13 17 -4 0 -13 -24 4 (B) 1 -3 -5 2 0 14 14 -5 0 -15 -24 7 (C) 1 -3 -5 2 0 14 14 -4 0 -15 -24 6 (D) 1 -3 -5 2 0 14 17 -5 0 -16 -24 7 (E) 1 -3 -5 2 0 14 14...