In Exercises 1–6, solve the equation Ax = b by using the LU factorization given for A. In Exercises 1 and 2, also solve Ax = b by ordinary row reduction.
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- part C Darrow_forwardSection 2.2 2.1. Solve the following difference equations: (a) Yk+1+Yk = 2+ k, (b) Yk+1 – 2Yk k3, (c) Yk+1 – 3 (d) Yk+1 – Yk = 1/k(k+ 1), (e) Yk+1+ Yk = 1/k(k+ 1), (f) (k + 2)yk+1 – (k+1)yk = 5+ 2* – k2, (g) Yk+1+ Yk = k +2 · 3k, (h) Yk+1 Yk 0, Yk = ke*, (i) Yk+1 Bak? Yk (j) Yk+1 ayk = cos(bk), (k) Yk+1 + Yk = (-1)k, (1) - * = k. Yk+1 k+1arrow_forwardIn Exercises 65–74, factor by grouping to obtain the difference of two squares. 6x + 9 – y? 12x + 36 – y? 65. x? 66. x2 67. x + 20xr + 100 68. x? + 16x + 64 – x4 69. 9x2 70. 25x? – 20x + 4 – 81y? 30x + 25 – 36y? 71. x* - x? – 2x – 1 72. x4 -х2 — бх — 9 x? + 4xy – 4y2 x²+ 10xy - 25y2 73. z? 74. z? - rarrow_forward
- Solve, z² – 4z + 5 = 0 Given that z1 = 3 + i, z2 = 4 – 3i, Z3 = -1+ 2i and z4 = -2 – 5i, determine in the form a + ib, where a, b E R, (real numbers), the following: (i) Z1 + Z2 ii) Z3Z4arrow_forwardFind matrix X: 3. 6 5 4 -2 *X= 18 49 -20 6arrow_forwardSection 2.2 2.1. Solve the following difference equations: (a) Yk+1+ Yk = 2+ k, (b) Yk+1 – 2yk = k³, (с) ук+1 "Yk = 0, (d) Yk+1 – Yk = 1/k(k+1), (e) Yk+1+ Yk = 1/k(k+1), (f) (k+2)yk+1 – (k + 1)yk = 5 + 2k – k², (g) Yk+1+ Yk = k + 2 · 3k, (h) Yk+1 – Yk = ke“, Yk = Bak*, = cos (bk), (k) Yk+1 + Yk = (-1)*, Yk – k. ,2k (i) Ук+1 (j) Yk+1 – aYk (1) Yk+1 k+1arrow_forward
- 4. Solve by Matrix Inversion. * For this number, solve using X = (A-1)B 2w – 2x + 3y + 4z = 33 3w – 5x – 7y + 3z = 11 4w + 3x – 4y – 5z = 3 5w + 4x + 6y – 2z = 45 1 Add filearrow_forwardQ/use Gaussian Elimination method to find the value of a, aa2 a3? 6a, + (155)a, +(5525)a, +(225125)a, = 6.000677 (155)a, +(5525)a, +(225125)a, +(9790625)a, =154.851 (5525)a, +(225125)a, +(9790625)a, +(442503125)a, = 5517.846 (225125)a, + (9790625)a, +(442503125)a, + (20515015625)a, = 224816.7arrow_forward2. Assume that all the operations are properly defined, solve the following equation for the unknown matrix X: ((A+X)" – 1) = B Use the result to evaluate X using the matrices A and 6 -2 B =arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt