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Problem 4. How many pivot columns must a 10 ~ 8 matrix have if its columns...
please answer both questions thank you! How many rows and columns must a matrix A have...
please answer both questions thank you!
How many rows and columns must a matrix A have in order to define a mapping from R into R by the rule T(x) Ax? Choose the correct answer below OA. The matrix A must have 7 rows and 7 columns. O B. The matrix A must have 9 rows and 7 columns OC. The matrix A must have 9 rows and 9 columns O D. The matrix A must have 7 rows and...
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer....
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 40 - 4 30 5 - 4 0 8 Choose the correct answer below O A. The matrix is not invertible. If the given matrix is A, the equation Ax = 0 has only the trivial solution. O B. The matrix is invertible. The given matrix has 2 pivot positions. OC. The matrix is invertible. The columns of the given matrix span R. OD....
8. Let A be a 5 x 4 matrix such that its reduced row echelon form...
8. Let A be a 5 x 4 matrix such that its reduced row echelon form has 4 pivot positions (leading entries). Which of the following statements is TRUE? a) The linear transformation T : R4 → R5 defined by T(X) = AX is onto. b) AX = 0 has a unique solution. c) Columns of A are linearly dependent. d) AX b is consistent for every vector b in R
Explain why the columns of an nxn matrix A are linearly independent when A is invertible...
Explain why the columns of an nxn matrix A are linearly independent when A is invertible Choose the correct answer below. O A. IFA is invertible, then for all x there is a b such that Ax=b. Since x = 0 is a solution of Ax0, the columns of A must be linearly independent OB. IA is invertible, then A has an inverse matrix A Since AA A AA must have linearly independent columns O C. If A is invertible,...
Problem 6. (10 points) Suppose that A is a matrix with seven columns and four rows....
Problem 6. (10 points) Suppose that A is a matrix with seven columns and four rows. Suppose that the columns of A span R. Determine the number of vectors needed to form a basis for the nullspace of T. Justify your answer.
747-38 1026 59% webwork.math.mcgill.ca Problem 5 linearly dependent linearly dependent At least one of the answers...
747-38 1026 59% webwork.math.mcgill.ca Problem 5 linearly dependent linearly dependent At least one of the answers above is NOT correct. 15 o to O- 40 (1 point) Let Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 15 B = 12 1-6 -9 -4 3 -101 -8 4 ] (a) Find the reduced row echelon form of the matrix B mref(B) = (b) How many...
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer....
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. - 3 30 20 6 -40 9 Choose the correct answer below. O A. The matrix is invertible. The given matrix has 2 pivot positions. O B. The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set. OC. The matrix is not invertible. If the given matrix is A, the equation Ax...
Suppose an 8 x 10 matrix A has eight pivot columns. Is Col A=R8? Is Nul...
Suppose an 8 x 10 matrix A has eight pivot columns. Is Col A=R8? Is Nul A=R2? Explain your answers. Is Col A =R8? A. Yes. Since A has eight pivot columns, dim Col A is 8. Thus, Col A is an eight-dimensional subspace of R8, so Col A is equal to R8 OB. No, the column space of Ais not R. Since A has eight pivot columns, dim Col A is 0. Thus, Col A is equal to 0....
Mark each statement as True or False and justify your answer. a) The columns of a...
Mark each statement as True or False and justify your answer. a) The columns of a matrix A are linearly independent, if the equation Ax = 0 has the trivial solution. b) If vi, i = 1, ...,5, are in RS and V3 = 0, then {V1, V2, V3, V4, Vs} is linearly dependent. c) If vi, i = 1, 2, 3, are in R3, and if v3 is not a linear combination of vi and v2, then {V1, V2,...
Suppose a 4x7 coeficient matrix for a system has four pivot columns. Is the system consistent?...
Suppose a 4x7 coeficient matrix for a system has four pivot columns. Is the system consistent? Why or why not? Choose the corect answer below. OA. There is a pivot position in each raw of the coefficient matrix. The auugmented matrix will have five columns and will not have a row of the form so the system is consistent. n o o 0 1 O B. There is a pivot position in each row of the coefficient matrix. The augmented...
please answer both questions thank you!
How many rows and columns must a matrix A have in order to define a mapping from R into R by the rule T(x) Ax? Choose the correct answer below OA. The matrix A must have 7 rows and 7 columns. O B. The matrix A must have 9 rows and 7 columns OC. The matrix A must have 9 rows and 9 columns O D. The matrix A must have 7 rows and...
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 40 - 4 30 5 - 4 0 8 Choose the correct answer below O A. The matrix is not invertible. If the given matrix is A, the equation Ax = 0 has only the trivial solution. O B. The matrix is invertible. The given matrix has 2 pivot positions. OC. The matrix is invertible. The columns of the given matrix span R. OD....
8. Let A be a 5 x 4 matrix such that its reduced row echelon form has 4 pivot positions (leading entries). Which of the following statements is TRUE? a) The linear transformation T : R4 → R5 defined by T(X) = AX is onto. b) AX = 0 has a unique solution. c) Columns of A are linearly dependent. d) AX b is consistent for every vector b in R
Explain why the columns of an nxn matrix A are linearly independent when A is invertible Choose the correct answer below. O A. IFA is invertible, then for all x there is a b such that Ax=b. Since x = 0 is a solution of Ax0, the columns of A must be linearly independent OB. IA is invertible, then A has an inverse matrix A Since AA A AA must have linearly independent columns O C. If A is invertible,...
Problem 6. (10 points) Suppose that A is a matrix with seven columns and four rows. Suppose that the columns of A span R. Determine the number of vectors needed to form a basis for the nullspace of T. Justify your answer.
747-38 1026 59% webwork.math.mcgill.ca Problem 5 linearly dependent linearly dependent At least one of the answers above is NOT correct. 15 o to O- 40 (1 point) Let Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 15 B = 12 1-6 -9 -4 3 -101 -8 4 ] (a) Find the reduced row echelon form of the matrix B mref(B) = (b) How many...
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. - 3 30 20 6 -40 9 Choose the correct answer below. O A. The matrix is invertible. The given matrix has 2 pivot positions. O B. The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set. OC. The matrix is not invertible. If the given matrix is A, the equation Ax...
Suppose an 8 x 10 matrix A has eight pivot columns. Is Col A=R8? Is Nul A=R2? Explain your answers. Is Col A =R8? A. Yes. Since A has eight pivot columns, dim Col A is 8. Thus, Col A is an eight-dimensional subspace of R8, so Col A is equal to R8 OB. No, the column space of Ais not R. Since A has eight pivot columns, dim Col A is 0. Thus, Col A is equal to 0....
Mark each statement as True or False and justify your answer. a) The columns of a matrix A are linearly independent, if the equation Ax = 0 has the trivial solution. b) If vi, i = 1, ...,5, are in RS and V3 = 0, then {V1, V2, V3, V4, Vs} is linearly dependent. c) If vi, i = 1, 2, 3, are in R3, and if v3 is not a linear combination of vi and v2, then {V1, V2,...
Suppose a 4x7 coeficient matrix for a system has four pivot columns. Is the system consistent? Why or why not? Choose the corect answer below. OA. There is a pivot position in each raw of the coefficient matrix. The auugmented matrix will have five columns and will not have a row of the form so the system is consistent. n o o 0 1 O B. There is a pivot position in each row of the coefficient matrix. The augmented...
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