Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer.1 -2 -60-43 26 0Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer.A. The matrix is invertible. The given matrix has 3 pivot positions.B. The matrix is not invertible. In the given matrix the columns do not form a linearly independent set.C. The matrix is invertible. The given matrix is not row equivalent to the nxn identity matrix.in R³.D. The matrix is not invertible. If the given matrix is A, the equation Ax=b has no solution for at least one b in

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Answered: Determine if the matrix below is…

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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Determine if the columns of the matrix form a linearly independent set. Justify your answer. Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) 0-8 3 16 1 - 14 5 -4 1-5 -2 -1 OA. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A form a linearly independent set. OB. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A do not form a linearly independent set. OC. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A form a linearly independent set.…
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Determine whether the statement below is true or false. Justify the answer. The equation Ax=b is consistent if the augmented matrix [a b] has a pivot position in every row. Choose the correct answer below. C A. This statement is false. The augmented matrix A b than rows. OB. This statement is true. The pivot positions in the augmented matrix [ A b] always occur in the columns that represent A. OC. This statement is true. If the augmented matrix [ A b] has a pivot position in every row, then the equation Ax=b has a solution for each b in R™. cannot have a pivot position in every row because it has more columns D. This statement is false. If the augmented matrix [ A b] has a pivot position in every row, the equation Ax = b may or may not be consistent. One pivot position may be in the column representing b.
Determine whether the following statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 1 A matrix row operation such as -R, +R, is not permitted because of the negative fraction. Choose the correct answer below. O A. The statement is true. O B. The statement is false. A true statement is "A matrix row operation such as - R. +R, is permitted regardless of the negative fraction." 8 O C. The statement is false. A true statement is "A matrix row operation such as --R, + R, is not permitted because of the fraction 1 O D. The statement is false. A true statement is "A matrix row operation such as -R, +R, is not permitted because of the-positive fraction."
Determine if the columns of the matrix form a linearly independent set. Justify your answer. Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) 0 -3 2 9 1 -7 4 -4 1-4-2 - 1 ⒸA. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A do not form a linearly independent set. B. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A do not form a linearly independent set. OC. If A is the given matrix, then the augmented atrix represents equation Ax = 0. The reduce echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A form a linearly independent set. O D.…
Determine if the columns of the matrix form a linearly independent set. Justify your answer. 237] -1 1-1 05 5
Determine if the columns of the matrix form a linearly independent set. Justify your answer. Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) A. If A is the given matrix, then the augmented matrix -4 -3 0 - 1 1 2 reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A form a linearly independent set. OC. If A is the given matrix, then the augmented matrix echelon form of this matrix indicates that Ax = 0 has do not form a linearly independent set. 1 1 represents the equation Ax = 0. The - 6 - 12 OB. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A form a linearly independent set. represents the equation Ax = 0. The reduced more than one solution. Therefore, the columns of A 0 6 O…

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