Question

In: Advanced Math

Given the matrix with rows [1,1,k 1] [1,k,1 1] [k,1,1 -2] Find the reduced row echelon...

Given the matrix with rows

[1,1,k 1]

[1,k,1 1]

[k,1,1 -2]

Find the reduced row echelon form of M, and explain how it depends on k. (b) Consider the linear system Ax = b for which the augmented matrix is A b = M. i. For what values of k is the system inconsistent? ii. For what values of k does the system have a unique solution?

Solutions

Expert Solution


Related Solutions

11. Given a row echelon form or the reduced row echelon form of an augmented matrix...
11. Given a row echelon form or the reduced row echelon form of an augmented matrix of a system of equations, determine the number of solutions the system has.
The following matrix is in reduced row echelon form. Decode from the matrix the solution of...
The following matrix is in reduced row echelon form. Decode from the matrix the solution of the corresponding system of linear equations or state that the system is inconsistent. (If the system is dependent assign the free variable the parameter t. If the system is inconsistent, enter INCONSISTENT.) 1 0 5 −4 0 1 −8 10 0 0 0 0 (x1, x2, x3) =
Is the following matrix in its reduced row echelon form? Explain your judgement.
Is the following matrix in its reduced row echelon form? Explain your judgement. 
for matrices, what is the difference between row reduced echelon form and an upper triangular matrix?
for matrices, what is the difference between row reduced echelon form and an upper triangular matrix?
Find the reduced row echelon form of the following matrices. Interpret your result by giving the...
Find the reduced row echelon form of the following matrices. Interpret your result by giving the solutions of the systems whose augmented matrix is the one given. [ 0 0 3 -1 5 1 0 0 4 2 4 1 3 0 -8 1 2 7 9 0 ]
Suppose R and R0 are 2 ⇥ 3 row-reduced echelon matrices and that the systems RX...
Suppose R and R0 are 2 ⇥ 3 row-reduced echelon matrices and that the systems RX = 0 and R’X = 0 have exactly the same solutions. Prove that R = R’ .
1. Make your own example of a 5-by-3 matrix that is in echelon row but do...
1. Make your own example of a 5-by-3 matrix that is in echelon row but do not reduce row echelon form. 2. Repeat for a 2-by-6 matrix 3. Make a 4-by-4 rref matrix whose first column contains only zeros
Find the basis for the row space, columnspace, and nullspace for the following matrix. Row 1...
Find the basis for the row space, columnspace, and nullspace for the following matrix. Row 1 {3,4,0,7} Row 2 {1,-5,2,-2} Row 3 {-1,4,0,3} Row 4 {1,-1,2,2}
(2) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal...
(2) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal matrix D such that P −1AP = D. Otherwise, explain why A is not diagonalizable. (a) A =   −3 0 −5                 0 2 0                 2 0 3 (b) A =   2 0 −1              1 3 −1              2 0 5 (c) A = 1 −1 2              −1 1 2               2 2 2
a.) Find a basis for the row space of matrix B. b.) Find a basis for the column space of matrix B.
For the given matrix B= 1 1 1 3 2 -2 4 3 -1 6 5 1 a.) Find a basis for the row space of matrix B. b.) Find a basis for the column space of matrix B. c.)Find a basis for the null space of matrix B. d.) Find the rank and nullity of the matrix B.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT