Question

when is a matrix said to be in echelon form?

Answer 1

In linear algebra, a matrix is in echelon form if it has the shape resulting from a Gaussian elimination. All rows consisting of only zeroes are at the bottom. The leading coefficient (also called the pivot) of a nonzero row is always strictly to the right of the leading coefficient of the row above it.

Answer 2

Here is Your Answer @AbdulHafeezAhmed,

Echelon Form

$\longmapsto$A matrix that has undergone Gaussian elimination is said to be in row echelon form or, more properly, "reduced echelon form" or "row-reduced echelon form." Such a matrix has the following characteristics:

• 1.) All zero rows are at the bottom of the matrix

• 2.) The leading entry of each nonzero row after the first occurs to the right of the leading entry of the previous row.

• 3.) The leading entry in any nonzero row is 1.

• 4.) All entries in the column above and below a leading 1 are zero.

Reduced Row Echelon form

• $\longmapsto$This is a special form of a row echelon form matrix. So A row echelon form is reduced row echelon form if it satisfies the following condition:

• $\longmapsto$A pivot or leading entry 1 in the row will be the only non-zero value in its columns. So all other values in the same column will have zero value.

Convert to Row Echelon Form

• $\longmapsto$We can convert any matrix into an row echelon form by applying multiple elementary operations. There are 3 main elementary operation.

$\longmapsto$The three elementary row operations are:

(Row Swap) Exchange any two rows. (Scalar Multiplication) Multiply any row by a constant. (Row Sum) Add a multiple of one row to another row.

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