Find the maximum value of
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- 3) Apply Jacobi's or Gauss Seidel method to the gieentem. Take the zero vector as the initial approximation and work with four significant digit accuracy until twosuccessive iterates agree within 0.001 in each variable. In each case, compare your answer with the exact solution found using any direct method you like. 3x1 - X2 -1 -XI +3x2 - X) -0 -X2 +3x3- x 1 -X3+ 3x 1arrow_forwardFind the maximum and minimum values, and a vector where each occurs, of the quadratic form subject to the constraint. z = x1? + 12x2²; 9×1² + 81x22 = 729 The constrained maximum of occurs when (x1, ×2) = and the constrained minimum of occurs when (X1, ×2) =arrow_forward(b) Find any values of x such that the vectors 4x 3. are parallel and 1 X-1 to each other.arrow_forward
- 3 = [ ¹₂ ], b = [ ³ ], c = [ ¹₁ ], d = [¯^¹'], and v = [¯2²], 5. Given vectors a = (a) Find all real numbers x₁, x2, x3, x4, such that x₁a + x₂b + x3c + x4d = v (b) Write [at least] one sentence about what you have done above using the following mathematical term: linear combination. (c) Write [at least] one sentence about what you have done above using the following mathematical term: span.arrow_forwardFind a general set of solution vectors x₂ = - 5x2 X₂ = x₁ + 3x₂arrow_forwardThe zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and V3 because 0 = 0v₁ + 0v₂ + Ov3. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of V₁, V₂, and v3. If not possible, enter IMPOSSIBLE.) V₁= (1, 0, 1), V₂ = (-1, 1, 2), V3 = (0, 3, 6) 0 = Need Help? Road It O Type here to search BA O E a CTICE ANOTHER Activate Windows Go to Settings to activate Windows. 70°F Sunarrow_forward
- If lā| = 12 and |6| = 3, what is the maximum value of a · b. Give examples of vectors d and b that satisfy these conditions and achieve this maximum.arrow_forwardUsing the inverses of the previous problem, find the solution of Ax = b and Bx = c for the vectors b = (3, 2, 1, 1, 4)^T and c = (1, 2, 1)^T , respectively.arrow_forwardThe zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v,, v2, and v, because 0 = Ov, + Ov, + Ov3. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v,, v, and v. If not possible, enter IMPOSSIBLE.) v = (1, 0, 1), v2 = (-1, 1, 2), v3 = (0, 9, 2) 0 = Need Help? Read Itarrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage