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....
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 0 3 - 4 0 2 -4 -9 4 Choose the correct answer below. O A. The matrix is not invertible. If the given matrix is A, the equation Ax=b has at least one solution for each b in R3. OB. The matrix is invertible. The given matrix has 3 pivot positions. C. The matrix is invertible. The columns of the given matrix span...
Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2 -1 01 0 - 1 3 1 1 -6 2 1 - 12 Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) O 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...
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,...
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,...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
a.) if A is an m*n matrix, such that Ax=0 for every vector x in R^n, then A is the m * n Zero matrix b.) The row echelon form of an invertible 3 * 3 matrix is invertible c.) If A is an m*n matrix and the equation Ax=0 has only the trivial solution, then the columns of A are linearly independent. d.) If T is the linear transformation whose standard matrix is an m*n matrix A and the...
Justify your answer: a) Could a set of three vectors in R5 span all of R5? You have to provide a short argument which shows why your answer is correct. b) Suppose A is a 3X3 matrix and b is a vector in R3 with the property that Ax =b has a unique solution. Explain why the columns of A must span all of R3.
12. a. If there is an n x n matrix D such that AD = 1, then there is also an n x n matrix C such that CA= 1. b. If the columns of A are linearly independent, then the columns of A span Rn. c. If the equation Ax = b has at least one solution for each bin Rn, then the solution is unique for each b. d. If the linear transformation (x) -> Ax maps Rn into Rn, then...
Let B be the standard basis of the space P2 of polynomials. Use coordinate vectors to test whether the following set of polynomials span P2. Justify your conclusion. 1-3t+ 2t?, - 4 + 9t-22, -1 + 412, + 3t - 6t2 Does the set of polynomials span P2? O A. Yes, since the matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position in each row, the set of coordinate vectors spans R3. By isomorphism between...