Let u = = [−6, −18, 6], v = [−4, -9, 10], and w = [4, 8, -12]. We want to determine if the set {u, v, w} is linearly independent or dependent. Construct the matrix A = [ whose rows are the three given vectors, and then reduce it to row echelon form using only three elementary row operations: First add Then add Finally add u times the first row to the second (in order to eliminate the leading entry of row two). times the first row to the third (in order to eliminate the leading entry of row three). times the new second row to the new third row (in order to eliminate the new leading entry of row three). From the reduced matrix, we conclude that: A. the set {u, v, w}| is linearly dependent O B. the set {u, v, w} is linearly independent C. we cannot tell if the set {u, v, w} is linearly independent or not

Let u = = [−6, −18, 6], v = [−4, -9, 10], and w = [4, 8, -12]. We want to determine if the set {u, v, w} is linearly independent or dependent. Construct the matrix A = [ whose rows are the three given vectors, and then reduce it to row echelon form using only three elementary row operations: First add Then add Finally add u times the first row to the second (in order to eliminate the leading entry of row two). times the first row to the third (in order to eliminate the leading entry of row three). times the new second row to the new third row (in order to eliminate the new leading entry of row three). From the reduced matrix, we conclude that: A. the set {u, v, w}| is linearly dependent O B. the set {u, v, w} is linearly independent C. we cannot tell if the set {u, v, w} is linearly independent or not

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Similar questions

Determine which columns of the following matrix are pivot columns. -2 -3 4 -4 2 6 -6 -2 0 -2 2 -2 2 Enter numbers of all pivot columns separating them by commas: For example, if the 1st, 2nd and 4th columns are the pivot columns then you should enter 1, 2, 4 as your answer.
Let A be a 5 x 4 matrix and b a nonzero vector in R5. We are told the system Ar = b has infinitely many solutions. List all possible ranks of the matrix A.
Write the system of equations as an augmented matrix + S 5d + 2r 136 4d + 6r 7d 6r - 7s - 6s - - - - TERENGT - 45 -311 - structor
Determine the order of the following matrix: [[8,4,-4,9],[-4,-4,1,-3],[-6,4,-8,-8],[3,5,4,5],[8,-6,-3,3]]
Find a non-zero vector V in the row space of the matrix -20 4 -9 -3 12 25 --5 -12 -4 16 V
What is a pivot column?
If Matrix A {(a b c), (x y z), (l m n)} = 4, what is the value of matrix B {(a b c), (2a 2b 2c), (l m n)}?use the matrices with the corrosponding orders of rows to find answer.
Write the system of equations as an augmented matrix -r 4b 250 - 2r + 7b 350 - - 4r + 156 + 150 - ||
Fill in the blanks of the resulting matrix after the given row operation is performed: -1 8 3 -1 7 -4R₁ 3 R₁ 381 3 -1 8 R₂+3R₁ -1 7 -4 -1 8 R₁-4R₂ 7 R₂ R₁