代数示例

$[\begin{array}{c} 4 & 2 \\ 0 & 1 \end{array}] + [\begin{array}{c} 5 & 9 \\ 8 & 2 \end{array}] = [\begin{array}{c} 9 & x \\ 8 & 3 \end{array}]$

解题步骤 1

加上相应元素。

$[\begin{array}{c} 4 + 5 & 2 + 9 \\ 0 + 8 & 1 + 2 \end{array}] = [\begin{array}{c} 9 & x \\ 8 & 3 \end{array}]$

解题步骤 2

Simplify each element.

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解题步骤 2.1

将 $4$ 和 $5$ 相加。

$[\begin{array}{c} 9 & 2 + 9 \\ 0 + 8 & 1 + 2 \end{array}] = [\begin{array}{c} 9 & x \\ 8 & 3 \end{array}]$

解题步骤 2.2

将 $2$ 和 $9$ 相加。

$[\begin{array}{c} 9 & 11 \\ 0 + 8 & 1 + 2 \end{array}] = [\begin{array}{c} 9 & x \\ 8 & 3 \end{array}]$

解题步骤 2.3

将 $0$ 和 $8$ 相加。

$[\begin{array}{c} 9 & 11 \\ 8 & 1 + 2 \end{array}] = [\begin{array}{c} 9 & x \\ 8 & 3 \end{array}]$

解题步骤 2.4

将 $1$ 和 $2$ 相加。

$[\begin{array}{c} 9 & 11 \\ 8 & 3 \end{array}] = [\begin{array}{c} 9 & x \\ 8 & 3 \end{array}]$

解题步骤 3

Write as a linear system of equations.

$9 = 9$

$11 = x$

$8 = 8$

$3 = 3$

解题步骤 4

Since $3 = 3$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying $11 = x$ .

代数 示例