有限数学示例

$[\begin{array}{c} 2.5 & 0 & 1.5 \\ 2.5 & 0 & 0 \\ 1.5 & 0 & 0 \end{array}]$

解题步骤 1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in column $2$ by its cofactor and add.

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解题步骤 1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

解题步骤 1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

解题步骤 1.3

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 2.5 & 0 \\ 1.5 & 0 \end{array} |$

解题步骤 1.4

Multiply element $a_{12}$ by its cofactor.

$0 | \begin{array}{c} 2.5 & 0 \\ 1.5 & 0 \end{array} |$

解题步骤 1.5

The minor for $a_{22}$ is the determinant with row $2$ and column $2$ deleted.

$| \begin{array}{c} 2.5 & 1.5 \\ 1.5 & 0 \end{array} |$

解题步骤 1.6

Multiply element $a_{22}$ by its cofactor.

$0 | \begin{array}{c} 2.5 & 1.5 \\ 1.5 & 0 \end{array} |$

解题步骤 1.7

The minor for $a_{32}$ is the determinant with row $3$ and column $2$ deleted.

$| \begin{array}{c} 2.5 & 1.5 \\ 2.5 & 0 \end{array} |$

解题步骤 1.8

Multiply element $a_{32}$ by its cofactor.

$0 | \begin{array}{c} 2.5 & 1.5 \\ 2.5 & 0 \end{array} |$

解题步骤 1.9

Add the terms together.

$0 | \begin{array}{c} 2.5 & 0 \\ 1.5 & 0 \end{array} | + 0 | \begin{array}{c} 2.5 & 1.5 \\ 1.5 & 0 \end{array} | + 0 | \begin{array}{c} 2.5 & 1.5 \\ 2.5 & 0 \end{array} |$

解题步骤 2

将 $0$ 乘以 $| \begin{array}{c} 2.5 & 0 \\ 1.5 & 0 \end{array} |$ 。

$0 + 0 | \begin{array}{c} 2.5 & 1.5 \\ 1.5 & 0 \end{array} | + 0 | \begin{array}{c} 2.5 & 1.5 \\ 2.5 & 0 \end{array} |$

解题步骤 3

将 $0$ 乘以 $| \begin{array}{c} 2.5 & 1.5 \\ 1.5 & 0 \end{array} |$ 。

$0 + 0 + 0 | \begin{array}{c} 2.5 & 1.5 \\ 2.5 & 0 \end{array} |$

解题步骤 4

将 $0$ 乘以 $| \begin{array}{c} 2.5 & 1.5 \\ 2.5 & 0 \end{array} |$ 。

$0 + 0 + 0$

解题步骤 5

化简行列式。

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解题步骤 5.1

将 $0$ 和 $0$ 相加。

$0 + 0$

解题步骤 5.2

将 $0$ 和 $0$ 相加。

$0$

有限数学 示例

有限数学示例