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Calculus and Its Applications (11th Edition)
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- Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)arrow_forwardDetermine whether each vector is a scalar multiple of z=(3,2,5). a v=(92,3,152) b w=(9,6,15)arrow_forwardFor which values of t is each set linearly independent? a S={(t,0,0),(0,1,0),(0,0,1)} b S={(t,t,t),(t,1,0),(t,0,1)}arrow_forward
- Plz answer all correctly asaparrow_forwardQ1. Show that the vectors x, =(1,2,4), x, = (2,-1,3), x, = (0,1,2) and x, =(-3,7,2) are linearly dependent and find the relation between them. Ans: 9x, - 12x, + 5х, - 5х, -0 Q2. If the vectors (0,1,a), (1, a,1) and (a,1,0) is linearly dependent, then find the value of a. Ans: 0,+/2 Q3. Find the eigen values and eigen vectors of the following matrices: 8 -6 2 (i) -6 7 [31 4] (ii) 0 2 6 0 o 5 -4 -4 3 Ans: (i) 0, 3, 15, k 2, ka (ii) 3, 2, 5, Q4. Verify Cayley-Hamilton theorem for the following matrix and hence compute A: [2 -1 1] A = -1 2 -1 I -1 2 [3 1 -1 Ans: 41 3 1 3 [2 11 Q5. Find the characteristic equation of the matrix A =0 1 0 and hence, compute A. Also find the matrix represented by A -5A" +7A“ - 3A +A* - SA' + 8A? - 2A +1. [8 5 5 [ 2 -1 -1 Ans: 2'-5a + 72 - 3 = 0, 0 3 0,A 3 55 8 3 -1 -1 10 5 Q6. Show that the matrix -2 -3 -4 has less than three linearly independent eigen vectors. Also 3 5 7 find them. Ans: A= 2,2,3. For i = 3, X, = [k,k,-2k] , for 2 = 2, X, = [5k,2k,-Sk] [i -1 2…arrow_forwardQ7) True or False, and Justify your answer. If v1, v2, ... V4 are in R* and v3 = 2v1 + v2, then {v1, V2, V3, V4} is linearly independent.arrow_forward
- Let L₁ be the line passing through the points Q₁=(−1, −3, 1) and Q₂=(−4, −6, 2). Find a value of k so the line L₂ passing through the point P₁ = P₁(−14, 12, k) with direction vector d=[-2, 6, −5]ª intersects with L₁. k = 0arrow_forward) Let B = {v₁ =, √₂ =, √3 =}. Determine whether B is linearly independent or linearly dependent.arrow_forward-2 as a linear combination of x 4 and y = -3 Express the vector v =arrow_forward
- Evaluate V(x² y + x y z?) · d r where C is the line segment from (1, – 1,0) to (2,1,3) | Select one: a. Non of them b. 43/2 с. 45/2 d. 49/2 е. 47/2arrow_forwardPlease help me solve, thank you. Don't reject my question. I just want to learn. It's my year one linear algebra question.arrow_forwardX = Find the vector equation for the line of intersection of the planes x - 5y + 5z = −5 and x + 5z = 1 -25 T +t Oarrow_forward
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