Find the matrix of the quadratic form8x²+7x²-3x² - 6x1X2 + 4X1X3 − 2x2x3a)b)c)d)8-3 2-3 7 -12 -1 -38-6 40 7 -200 -3-347/242 -3/27/2 -3/2 -18 2-327 -1-3 -1 -3

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Answered: Find the matrix of the quadratic form…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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factor completely 1). X3 + X2 + 2X + 2 2). 4y3-256y
(Left nullspace) Add the extra column b and reduce A to echelon form: [1 2 3 [Ab] 4 5 6 bi 1 b₂ → 2 3 0-3 -6 7 8 9 b3 0 00 bi b2-4b₁ b3 - 2b2 + b₁ A combination of the rows of A has produced the zero row. What combination is it? (Look at b3 - 2b2+ b₁ on the right side.) Which vectors are in the nullspace of AT and which vectors are in the nullspace of A?
Let u = = X₁ = -4 4 V= 5 x2 = (Simplify your answers.) and w= operations) to find x₁ and x₂ that satisfy the equation 0 - 41 -8 It can be shown that -5u-4v-w=0. Use this fact (and no row -4 5 5 4 4 - 3 X2 0 - 41 -8
3. Factor by g) 6xy² = (3x) (?) h) 25a³b² = (5a²b²) (?) i) 6x + 6y + 6p 4. Factor: identifying a common factor in each term. j) x(x+2) + y (x + 2)-5(x + 2) k) 5y²-10y³ l) ax + ay + az 5. Factor: m) yx(y+1) + 4x(y + 1) - 5(y + 1) n) 6p²-3p³ 0) 4x4 + 2x T
Find the matrix of the quadratic form 2x1? + 3x2² – x32 + 4x1x2 – 2 x1x3 + 6x2x3 2 2 -2 1 (a) 2 3 (b) -2 3 3 -1 3 -1 1 3 -1 2 -2 -1] [2 2 1 (d) 2 l1 -2 3 3 3 -3 [-1 3 -1. -3 -1.
Find the matrix of the quadratic form S+7-3r-6r ay+4rd-2r2y a) 2-1 b) 7-2 7/2 -3/2 3. c) 7/2 -3/2 2. d) 410
Please do 1a 2a and 3a
Let u = -6 -7 , V= 6 3 -2 2 X₁ x2 (Simplify your answers.) , and w= - 3 35. It can be shown that -3u-7v-w=0. Use this fact (and no row operations) to find x₁ and x₂ that satisfy the equation - 32 -6 3 -7-2 6 2 X₁ X2 - 3 35 . - 32
Let u = -7 5 -6 , V = -7 7 equation 5-2 -6 6 7 -2 6 X₁ x2 X₁ X2 (Simplify your answers.) and w= - 14 -11 - 12 - 14 - 11 . It can be shown that -5u-7v-w=0. Use this fact (and no row operations) to find x₁ and x₂ that satisfy the - 12

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Find the matrix of the quadratic form 8x²+7x²-3x² - 6x1X2 + 4X1X3 − 2x2x3 a) b) c) d) 8-3 2 -3 7 -1 -3 832 ܘܘ ܕܢ ܝܐ 2 -1 8-6 0 0 4 7 -2 910 0 -3 4 7/2 2 -3/2 -1 -3 4 7/2 -3/2 8 2-3 2 7 -1 -3 -1 -3