11. 11. a) Let Write b as a linear combination of the column vectors a1 and a2.

Question

11.

11. a) Let Write b as a linear combination of the column vectors a1 and a2. Use b as a linear combination of the column vectors a1 and a2 to determine a solution to the linear system Ax = b. Does the system have any other solutions? Explain. Write c as a linear combination of the column vectors a1 and a2. n geq 4. C) Given: Show that An = O for Compute A2 and A3. What will A2n and A2n+1 t urn out to be? b) Let

Explanation / Answer

a) row operation we get R2----->R2+R1 R3----->R3+R1 R4----->R4+R1 by taking 1/2 common we get A =1/2 [1 -1 -1 -1] [0 0 0 0] [0 0 0 0] [0 0 0 0 ] A^2 = A^3 = A^2n = A^2n+1 = 0 b) by checking for n we can do this a = [ 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 0, 0, 0, 0] a = 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 >> b = a^4 b = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 >> c = a^3 c = 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 >> d = a^2 d = 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 >> e = a^-1 Warning: Matrix is singular to working precision. e = Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf >> f = a^6 f = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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