1. Determine which of the following matrices are invertible. Use the Invertible Matrix Theorem (or other...
Each of the matrices given below is an augmented matrix of a system linear equations. In each case decide if the system has no solutions, exactly one solution, or infinitely many solutions. Try to perform as few computations as possible. A= ſi 2 0 1 Lo 0 1 3 0 1 1 0 1 1 1 0 B= ſi 0 0 3 47 0 1 3 1 1 LO 0 1 1 0 C= [100 0 1 0 Lo 0...
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...
) Use the theorem on triangular matrices, to determine the deter minant of the matrix (it is a one liner): (e) Use the theorem on triangular matrices, to determine the deter- minant of the matrix (it is a one liner) 2 3 4 A=1031 0 0 1 (f) Use the theorem on triangular matrices, to determine the deter- minant of the matrix (it is a one liner) 3 4
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....
5 points 1. True of False: a. if A is an n x1 matrix and B is a 1 xn matrix, then AB is an n xn matrix. b. if A is an n x1 matrix and B is a 1 x n matrix, then BA is not defined. 20 points 2. Use the Invertible Matrix Theorem to determine which of the matrices below are invert- ible. Use as few calculations as possible. Justify your answers. [34 01 4 5...
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...
3 seperate questions multiple choice Determine which of the following matrices are in RREF. ſi 0 0 27 i) 0 2 0 3 0 1 1 4 ſi 0 1 0] i) 0 1 1 0 0 0 0 1 [1 0 -1 2 ii) 0 1 07 0 o [1 0 0 2 iv) 0 1 0 1 0 0 1 0 0 0 1 iv only ii and iii ii and iv i and ii For the given...
(b) In each case below, state whether the statement is true or false. Justify your answer in each case. (i) A+B is an invertible 2×2 matrix for all invertible 2×2 matrices A, B. [4 marks] (ii) If A is an n×n invertible matrix and AB is an n×n invertible matrix, then B is an n × n invertible matrix, for all natural numbers n. [4 marks] (iii) det(A) = 1 for all invertible matrices A that satisfy A = A2....
for (a) plz thank u!!? 14. For it is given that 1-2 is an invertible matrix such that 1 0 01 AQ A-2 0 0 0 1 0] Let A ((1. 2,0), (0,0, D), (0,0, 0)). Find a basis B of R3 such that the m transition from B to A is matrix of 10 01 D2-0 1 0 and an invertible P such that PAQ D2. (Hint: See the proof of Theorem 3.46.) 15. For each matrix A below,...
could u help me for this one?? 14. For it is given that 1-2 is an invertible matrix such that 1 0 01 AQ A-2 0 0 0 1 0] Let A ((1. 2,0), (0,0, D), (0,0, 0)). Find a basis B of R3 such that the m transition from B to A is matrix of 10 01 D2-0 1 0 and an invertible P such that PAQ D2. (Hint: See the proof of Theorem 3.46.) 15. For each matrix...