線形代数例

$[\begin{array}{c} 4 & 0 \\ 5 & 2 \end{array}] [\begin{array}{c} 3 & 7 \\ 1 & x \end{array}] = [\begin{array}{c} 12 & 28 \\ 17 & 69 \end{array}]$

ステップ 1

$[\begin{array}{c} 4 & 0 \\ 5 & 2 \end{array}] [\begin{array}{c} 3 & 7 \\ 1 & x \end{array}]$ を掛けます。

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ステップ 1.1

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is $2 \times 2$ and the second matrix is $2 \times 2$ .

ステップ 1.2

1番目の行列の各行と2番目の行列の各列を掛けます。

$[\begin{array}{c} 4 \cdot 3 + 0 \cdot 1 & 4 \cdot 7 + 0 x \\ 5 \cdot 3 + 2 \cdot 1 & 5 \cdot 7 + 2 x \end{array}] = [\begin{array}{c} 12 & 28 \\ 17 & 69 \end{array}]$

ステップ 1.3

すべての式を掛けて、行列の各要素を簡約します。

$[\begin{array}{c} 12 & 28 \\ 17 & 35 + 2 x \end{array}] = [\begin{array}{c} 12 & 28 \\ 17 & 69 \end{array}]$

ステップ 2

Write as a linear system of equations.

$12 = 12$

$28 = 28$

$17 = 17$

$35 + 2 x = 69$

ステップ 3

Since $17 = 17$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying $35 + 2 x = 69$ .

線形代数 例

線形代数例