For Problem 16-18, determine whether the given set of
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- Solve for X in the Equation, given A=-401-532 and B=12-2144 a 3X+2A=B b 2A5B=3X c X-3A+2B=0 d 6X4A-3B=0arrow_forward3. If a = 3x - 5ỹ and b = -2x +9y, write the vector 5a-86 in terms of x and yarrow_forwardSuppose that A= 2 6 2 [-1 1 1] Describe the solution space to the equation Ax = 0. Describe the solution space to the equation Ax = b where b : Are there any vectors b for which the equation Ax = b is inconsistent? Explain your answer. Do the columns of A span R? Explain your answer.arrow_forward
- Solve the following exercises, you will need to show all your work to receive full credit. Consider the matrix, 2 1 -2 2 3 -4 1 1 1 - Knowing that f(t) = (t – 1)²(t - 2) is the characteristic polynomial, do the following: 1. find a basis of eigenvectors; 2. Find P such that P- AP is a diagonal matrix D. Give Darrow_forwardLet -0-0-0-0 V2 = w= -5 = -2 = = If possible, express w as a linear combination of the vectors V₁, V2 and v3. Otherwise, enter DNE. For example, the answer w = 4v₁ + 5v2 + 603 would be entered 4v1 + 5v2 + 6v3.arrow_forwardIf k is a real number, then the vectors (1, k), (k, k+ 56) are linearly independent precisely when k # a, b, where a = , 6 = and a < b.arrow_forward
- 4. a. If 37– 2ỷ = đ and 53 – 3ỷ = b, express the vectors i and y in terms of a and b. %3D b. Solve for a, b, and c: (2, –1, c) + (a, b, 1) – 3(2, a, 4) = (-3, 1, 2c). %3Darrow_forward1. Find all solutions: 2. In what ways can 88-8 and be written x+y ==0 a as a linear combination of [] [] [4], and ² 3. Show that the vector 2 is NOT contained in the span of the following three vectors 6 4. For which b are the vectors -0.0 x+2y+z=5 2x+3y-z=3 independent?arrow_forwardIf v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.arrow_forward
- 6. 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_forwardIf the answer to (a) is yes, express the following two vectors each as linear A Given the following two vectors I=and V2 Are these two vectors linearly independent? 1. combination of UrL and Usarrow_forwardIf k is a real number, then the vectors (1,k),(k,7k+8) are linearly independent precisely when k ≠ a,b, where a = ? and b = ?, and a<barrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning