Linear Algebra Examples

⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & 0 0 & 0 & 1 125 x^{3} & - 75 x^{2} & 15 x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 125 x^{3} & - 75 x^{2} & 15 x \end{array}]$

Step 1

A matrix is a rectangular arrangement or array of elements. The dimensions of a matrix,

m \times n

$m \times n$ , identify how many rows and columns a matrix has.

m

$m$ represents the number of rows and

n

$n$ represents the number of columns. Assuming that the matrix name is

A

$A$ , the matrix dimensions are written as

A_{m \times n}

$A_{m \times n}$ .

Step 2

The number of rows is

3

$3$ .

m = 3

$m = 3$

Step 3

The number of columns is

3

$3$ .

n = 3

$n = 3$

Step 4

The given matrix has dimensions

m \times n = 3 \times 3

$m \times n = 3 \times 3$ .

A_{m \times n} = A_{3 \times 3}

$A_{m \times n} = A_{3 \times 3}$