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- For matrices X=[xyzw] and 0=[0000], find the matrix 0X.arrow_forwardThe following question is from linear algebra : Factors the vector (6, -5, -1)t into three components a,b,c that satisfy the following conditions: a depends on (2,0,1)t, b depends on (1,2, 0)t and c is orthogonal to a and b. Please show it step by step.arrow_forwardThe following question is from linear algebra first year: Factors the vector (6, -5, -1)t into three components a,b,c that satisfy the following conditions: a depends on (2,0,1)t, b depends on (1,2, 0)t and c is orthogonal to a and b. Please show it step by step. Can we get integers as answers?arrow_forward
- For each of the following lists of vectors in R³, determine whether or not the first vector can be expressed as a linear combination of the other two. (a) (-2, 0,3), (1, 3,0), (2, 4, -1) (b) (1,2,3), (-3, 2, 1), (2, -1, −1) (c) (3, 4, 1), (1, -2, 1), (−2, —1, 1)arrow_forwardA B -1 -2 C D E -4 -5 -3 F 1 GHI 2 3 L JK -1 -2 4 5 P Q R 2 3 1 MNO -5 -4 -3 TU S 4 5 -1 V -2 W X -3 -4 Y 1 N 2 Use the table above to create two vectors in 2-Space: * and y Let * be a vector representative of the first two letters in your given name and y represent the first two letters of your surname. (Ex. Albert Einstein: x= [-1, -2] and y = [-5,4]) My vectors are 2 = [-1₁-4] and j = [ -5, -2] Use the table above to create two vectors in 3-Space: è and f Let è be a vector representative of the first three letters in your given name and represent the first three letters of your surname. (Ex. Albert Einstein: € = [-1, -2, -2] and f = [-5,4,-4]) My vectors are è = [-1,-4, 2] and f= [-5, -2₁ -2] e 1. Angle Between Vectors and Projects a) Use the dot product to verify the type of angle connecting the vectors and y (acute, right or obtuse). b) Find the angle connecting the vectors and y in two different ways. c) Use the dot product to verify the type of angle connecting the vectors e and…arrow_forwardLet A = - - 3 [1] [2] and b = 3 9 b2 Show that the equation Ax = b does not have a solution for some choices of b, and describe the set of all b for which Ax=b does have a solution. How can it be shown that the equation Ax=b does not have a solution for some choices of b? A. Find a vector x for which Ax=b is the identity vector. B. Row reduce the augmented matrix [ A b] to demonstrate that A b has a pivot position in every row. C. Find a vector b for which the solution to Ax=b is the identity vector. D. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row. E. Row reduce the matrix A to demonstrate that A has a pivot position in every row.arrow_forward
- Given the following vectors A = 4a +3a - 2a y B=a + 5a +7a_ X y C=-2a-4a +6a X y Evaluate |AX (BXC)|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_forwardSolve 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_forward
- List a set of three vectors in R2 that spans R2 from which you can any remove any two of the vectors and still span R² with the remaining one vector. List a set of three vectors in R2 that spans R2 from which you can remove either of two particular vectors and still span R² with the remaining two vectors. However, if you remove the third vector, the remaining two vectors will not span R². State which vectors can and can't be removed. List a set of three vectors in R² that spans R² from which you can remove two particular vectors and still span R² with the remaining one vector. State which vectors can be removed. List a set of three vectors in R2 that spans R2 from which you cannot remove any one of the vectors and still span R2 with the remaining two vectors.arrow_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_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
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,