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For Problems, 25-31, determine a linearly independent set of
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- Ifv = [ -2, 4], compute and draw 2v, 1/2 v, and -2v.arrow_forward6. Consider the following system of four linear equations in five variables. 2x1 + 4x2 – 2x3 + 2x4 + 4x3 = 2 xị+ 2x2 – x3+ 2x4 = 4 3x1 + 6x2 – 2x3 + x4 + 9x5 = 1 5x1 + 10r2 – 4x3 + 5x4 + 9x5 = 9 | (a) Write a vector equation that is equivalent to this linear system, and a matrix equation that is equivalent to this linear system. (b) Determine the solution set of this linear system, and express it in parametric vector form.arrow_forwardFor two linear equations in three unknowns x, y, z, the row picture will show (2 or 3) (lines or planes) in (2 or 3)-dimensional space. The column picture is in (2 or 3)dimensional space. The solutions normally lie on a __ .arrow_forward
- Find a general set of solution vectors x₂ = - 5x2 X₂ = x₁ + 3x₂arrow_forwardGraph the two vectors x= (5, 1,3) and y=(-1,3,1arrow_forwardThe following leLPP Max Z-SX - 72 6X3 (lundrede of dollars S) X1+ 4X2 23 60 2X1- 2X2 3X3 40 XT• 2X2. 2X3 30 (production capacity: hours) (warehouse capacity: hundrede of sq. ) (demand for 6 or. glassee; undreds of cesos) Basis CB 5X1 7X2 6X3 51 S2 RHS X2 S1 X1 0.6 0.6 10 -1 1 1. 10 0. 10 7. 8.5 7.6 120 C-Z -2.5 -1.5 -2 What effect on the optimal solution (value of Z) ,if we change the profit of X3 from 6 to $2.1 ?arrow_forward
- Let V₁ = 6 , V₂ = 1 -3 -1 0 combination of V₁, V₂ and V3. , V3 = 2 5 -5 , V4 = -26 -9 -1 -3 Express V4 as a lineararrow_forwardThis is from section 1.3 "Homogenous Equations" out of the textbook titled "Linear Algebra With Applications". If you could provide step by step instructions in how to do these problems, I would be grateful. Thanks!arrow_forwardFor each problem, give an example of a set of vectors in R4 that meet criteria and briefly justify your answers. Give different examples than your classmates. 1. Linearly independent and spans all of R¹. 2. Linearly independent but does not span all of R4. 3. Linearly dependent and spans all of R¹. 4. Linearly dependent and does not span all of R4.arrow_forward
- Find the set of all solution vectors of the following system of linear equations and write in form X = X₁ + Xp² where Xh is the homogeneous solution(s) and x is a particular solutions. р 2x₁ - x₂ + 3x3 =-3 4x₁+2x₂ −X4 = 1 -arrow_forwardGiven the following vectors A = 4a +3a - 2a y B=a + 5a +7a_ X y C=-2a-4a +6a X y Evaluate |AX (BXC)|arrow_forwardFind two linearly independent solutions of y" + 1xy = 0 of the form Y1 1+ azx³ + a6x® + · ... Y2 = x + b4x4 + b7x + . ... Enter the first few coefficients: Az = -5/6 help (numbers) a6 help (numbers) b4 help (numbers) b7 help (numbers) I| ||arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning