Aljabar Linear Contoh

$[\begin{array}{c} 2 & 3 & 4 \\ 1 & 2 & 1 \\ 3 & 1 & 2 \end{array}] = [\begin{array}{c} x \\ y \\ z \end{array}]$

Langkah 1

Kernel dari transformasi adalah vektor yang membuat transformasinya sama dengan vektor nol (prabayangan dari transformasi).

$[\begin{array}{c} x \\ y \\ z \end{array}] = 0$

Langkah 2

Buat sistem persamaan dari persamaan vektor.

$x = 0$

$y = 0$

$z = 0$

Langkah 3

Write the system as a matrix.

$[\begin{array}{c} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{array}]$

Langkah 4

Use the result matrix to declare the final solution to the system of equations.

$x = 0$

$y = 0$

$z = 0$

Langkah 5

Write a solution vector by solving in terms of the free variables in each row.

$[\begin{array}{c} x \\ y \\ z \end{array}] = [\begin{array}{c} 0 \\ 0 \\ 0 \end{array}]$

Langkah 6

Write as a solution set.

${[\begin{array}{c} 0 \\ 0 \\ 0 \end{array}]}$

Langkah 7

Kernel dari $M$ adalah subruang ${[\begin{array}{c} 0 \\ 0 \\ 0 \end{array}]}$ .

$K (M) = {[\begin{array}{c} 0 \\ 0 \\ 0 \end{array}]}$