Question

Find the pivot position of the following mahix
State whether it is invertible or not.
A=1. 3. 3
1. 4. 4.
1. 3. 4​

Answer 1

Reduced row echelon form (Gauss-Jordan elimination)collapse all in page

Syntax

R = rref(A)

R = rref(A,tol)

[R,p] = rref(A)

Description

example

R = rref(A) returns the reduced row echelon form of A using Gauss-Jordan elimination with partial pivoting.

R = rref(A,tol) specifies a pivot tolerance that the algorithm uses to determine negligible columns.

example

[R,p] = rref(A) also returns the nonzero pivots p.

Examples

collapse all

Reduced Row Echelon Form of Matrix

Create a matrix and calculate the reduced row echelon form. In this form, the matrix has leading 1s in the pivot position of each column.

A = magic(3)

A = 3×3

8 1 6

3 5 7

4 9 2

RA = rref(A)

RA = 3×3

1 0 0

0 1 0

0 0 1

The 3-by-3 magic square matrix is full rank, so the reduced row echelon form is an identity matrix.

Now, calculate the reduced row echelon form of the 4-by-4 magic square matrix. Specify two outputs to return the nonzero pivot columns. Since this matrix is rank deficient, the result is not an identity matrix.

Answer 2

$\huge\underbrace\mathfrak \red{ANSWER }$

Reduced row echelon form (Gauss-Jordan elimination)collapse all in page

Syntax

R = rref(A)

R = rref(A,tol)

[R,p] = rref(A)

Description

example

R = rref(A) returns the reduced row echelon form of A using Gauss-Jordan elimination with partial pivoting.

R = rref(A,tol) specifies a pivot tolerance that the algorithm uses to determine negligible columns.

example

[R,p] = rref(A) also returns the nonzero pivots p.

Examples

collapse all

Reduced Row Echelon Form of Matrix

Create a matrix and calculate the reduced row echelon form. In this form, the matrix has leading 1s in the pivot position of each column.

A = magic(3)

A = 3×3

8 1 6

3 5 7

4 9 2

RA = rref(A)

RA = 3×3

1 0 0

0 1 0

0 0 1

The 3-by-3 magic square matrix is full rank, so the reduced row echelon form is an identity matrix.

Now, calculate the reduced row echelon form of the 4-by-4 magic square matrix. Specify two outputs to return the nonzero pivot columns. Since this matrix is rank deficient, the result is not an identity matrix.

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