Determine if b is a linear combination of the vectors formed from the columns of the matrix A.Choose the correct answer below.A =- 5 - 205 3- 10 31213b= -78A. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in the first column, the secondentry in the second column, and the third entry in the third column.B. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in the first column and thesecond entry in the second column. There are no pivots in the third and fourth columns.C.Vector b is not a linear combination of the vectors formed from the columns of the matrix A. There is no solution to the linear system corresponding to the matrix AbD. Vector b is not a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are only in the first entry in the first column andthe second entry in the second column. There are no pivots in the third and fourth columns.

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Answered: Determine if b is a linear combination…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Can each vector in R* be written as a linear combination of the columns of the matrix A? Do the columns of A span R*? 3 1 7 - 12 - 1 - 1 A = - 4 - 2 2 0 - 10 20 0 2 - 1 Can each vector in R be written as a linear combination of the columns of the matrix A? Select the correct choice below and fill in the answer box to complete your choice, (Type an integer or decimal for each matrix element.) O A. No, because the reduced echelon form of A is O B. Yes, because the reduced echelon form of A is Help me solve this View an example Get more help - Clear all Check answer 82 9+ G 99+ W ENG DELL DII F3 prt sc F1 F4 FS beme end F7 F9 insert dele F10 F11 F12 %23 %2$ & 2 3 4 5 6 8
Determine whether the statement below is true or false. Justify the answer. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax=b has at least one solution. Choose the correct answer below. O A. This statement is false. If the equation Ax=b has infinitely many solutions, then the vector b cannot be a linear combination of the columns of A. O B. This statement is true. The equation Ax=b is unrelated to whether the vector b is a linear combination of the columns of a matrix A. O C. This statement is true. The equation Ax=b has the same solution set as the equation X₁ a₁ + x₂a₂+...+xa = b. ▶ O D. This statement is false. If the matrix A is the identity matrix, combination of the columns of A. the equation = b has at least one solution, but b is not a linear
What is a pivot column?
Use a graphing utility or computer software program with matrix capabilities to write v as a linear combination of u1, U2, U3, U4, ug and ug. Then verify your solution. u1 = (4, 4, -4, -3, 1, 3) u2 = (3, -4, 3, -4, 2, 4) u3 = (3, 4, -2, -3, -2, 1) U4 = (4, 2, -4, 4, 1, 1) u5 = (4, -4, -4, 2, -3, 4) U6 = (4, 4, -2, 4, 1, 1) v = (16, 68, -15, -6, 24, -7) V =
Use a graphing utility or computer software program with matrix capabilities to write v as a linear combination of u1, U2, U3, U4, Ug and ug. Then verify your solution. u1 = (1, 1, -4, -4, 3, 4) u2 = (4, -3, 1, -1, 1, 4) u3 = (0, 4, -3, -2, -4, 1) U4 = (4, 3, -4, 3, 4, 3) U5 = (4, -2, -4, 2, -4, 4) U6 = (3, 4, -4, 3, 3, 4) v = (-6, 42, -20, -18, 51, 11) V =
Write a vector equation 81-8181-81 y+ that is equivalent to the system of equations: -2x + 6y + 7z 2x +9y + 7% + Y x 4 = -9 6% = -6 = =
If the columns of the matrix A = -1 are orthogonal, then -1 a. aj = 2 b. a = -2 O c. aj = = -1 O d. a1 = 1 Clear my choice 2.

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