Let the coefficient matrix be in reduced echelon form with a pivot in each column, since each matrix is equivalent to one and only one reduced echelon matrix. Construct a matrix with the dimensions determined in the previous step that is in reduced echelon form and has a pivot in each column.

Constructed matrix

012

121 A

278

⇒

121

012 A1

278

⇒

121

012 A2

036

Step-by-step explanation:

Echelon Forms

A matrix is in row echelon form (ref) when it satisfies the following conditions.

1. The first non-zero element in each row, called the leading entry, is 1.

2. Each leading entry is in a column to the right of the leading entry in the previous row.

3. Rows with all zero elements, if any, are below rows having a non-zero element.

A matrix is in reduced row echelon form (rref) when it satisfies the following conditions.

The matrix is in row echelon form (i.e., it satisfies the three conditions listed above).

The leading entry in each row is the only non-zero entry in its column.

A matrix in echelon form is called an echelon matrix. Matrix A and matrix B are examples of echelon matrices.

1234

0013

0001

0000

A

1200

0010

0001

0000

B

Matrix A is in row echelon form, and matrix B is in reduced row echelon form.

How to Transform a Matrix Into Its Echelon Forms

Any matrix can be transformed into its echelon forms, using a series of elementary row operations. Here's how.

1. Pivot the matrix

Find the pivot, the first non-zero entry in the first column of the matrix.

2. Interchange rows, moving the pivot row to the first row.

Multiply each element in the pivot row by the inverse of the pivot, so the pivot equals 1.

3. Add multiples of the pivot row to each of the lower rows, so every element in the pivot column of the lower rows equals 0.

4. To get the matrix in row echelon form, repeat the pivot

Repeat the procedure from Step 1 above, ignoring previous pivot rows.

5. Continue until there are no more pivots to be processed.

To get the matrix in reduced row echelon form, process non-zero entries above each pivot.

Identify the last row having a pivot equal to 1, and let this be the pivot row.

Add multiples of the pivot row to each of the upper rows, until every element above the pivot equals 0.

Moving up the matrix, repeat this process for each row.

To illustrate the transformation process, let's transform Matrix A to a row echelon form and to a reduced row echelon form.

012

121 A

278

⇒

121

012 A1

278

⇒

121

012 A2

036

binomial distribution

median= 2

range = 7-0 = 7

how to find median?

no. of term=28

median=(28+1)/2=14.5th term

the 14th and 15th term are 2, therefore the median is (2+2)/2 = 2

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.