Question

In: Advanced Math

For each of the following matrices, find a minimal spanning set for its Column space, Row...

For each of the following matrices, find a minimal spanning set for its Column space, Row space,and Nullspace. Use Octave Online to get matrix A into RREF.

A = [4 6 10 7 2; 11 4 15 6 1; 3 −9 −6 5 10]

Solutions

Expert Solution

there is one pivot entry at first second and fourth column so a basis for the column space is

the basis for the row space is

reduced system is

general solution is

the basis for the null space is

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

For the following matrices, first find a basis for the column space of the matrix. Then...

For the following matrices, first find a basis for the column space of the matrix. Then use the Gram-Schmidt process to find an orthogonal basis for the column space. Finally, scale the vectors of the orthogonal basis to find an orthonormal basis for the column space. (a) [1 1 1, 1 0 2, 3 1 0, 0 0 4 ] b) [?1 6 6, 3 ?8 3, 1 ?2 6, 1 ?4 ?3 ]

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.

How are the column space and the row space of a matrix A related to the...

How are the column space and the row space of a matrix A related to the column space and row space of its reduced row echelon form? How does this prove the column rank of A equals the row rank?

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}

Write the following matrices into row echelon form.

Exercise1. Write the following matrices into row echelon form.

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 ]

Exercise1. Write the following matrices into row echelon form.

Exercise1. Write the following matrices into row echelon form. (a) A=⎛⎜⎝1132−22100474⎞⎟⎠A=(1132−22100474) (c) C=⎛⎜⎝121457210121331578⎞⎟⎠C=(121457210121331578) (b) B=⎛⎜⎝234304131⎞⎟⎠B=(234304131) (d) D=⎛⎜ ⎜ ⎜⎝11111−11−1−1−111−11λλ⎞⎟ ⎟ ⎟⎠

Find the characteristics and the minimal polynomial of the following matrices over R, then deduce the their corresponding Jordan Canonical Form J.

Find the characteristics and the minimal polynomial of the following matrices over \( \mathbb{R} \), then deduce the their corresponding Jordan Canonical Form J. A=\( \begin{pmatrix}1&-1&-1\\ 0&0&-1\\ 0&1&2\end{pmatrix}\: \)

Find the characteristics and the minimal polynomial of the following matrices over R , then deduce the their corresponding Jordan Canonical Form J.

Find the characteristics and the minimal polynomial of the following matrices over \( \mathbb{R} \), then deduce the their corresponding Jordan Canonical Form J. B=\( \begin{pmatrix}2&-1&-1&2\\ 0&1&-1&2\\ 2&-5&-1&6\\ 1&-3&-2&6\end{pmatrix} \)

Find the characteristics and the minimal polynomial of the following matrices over R, then deduce their corresponding Jordan Canonical Form J.

Find the characteristics and the minimal polynomial of the following matrices over R, then deduce their corresponding Jordan Canonical Form J. C=\( \begin{pmatrix}1&1&0&0\\ -1&-1&1&0\\ 0&1&1&0\\ -1&-1&1&1\end{pmatrix} \)

Subjects