线性代数示例

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

解题步骤 1

变换核是使变换等于零向量（变换厡像）的一个向量。

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

解题步骤 2

从向量方程创建一个方程组。

$x = 0$

$y = 0$

$z = 0$

解题步骤 3

Write the system as a matrix.

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

解题步骤 4

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

$x = 0$

$y = 0$

$z = 0$

解题步骤 5

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

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

解题步骤 6

Write as a solution set.

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

解题步骤 7

$M$ 的核心是子空间 ${[\begin{array}{c} 0 \\ 0 \\ 0 \end{array}]}$ 。

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

线性代数 示例