矩阵的数乘法则（C008）

问题

已知，矩阵

A

=

{(a_{i j})}_{m \times n}

λ

为实数.

则， $λ A$ $=$ $?$

[A].

λ A

=

(\begin{array}{ccc} λ a_{11} & \dots & a_{1 n} \\ ⋮ & ⋮ \\ λ a_{m 1} & \dots & a_{m n} \end{array})

[B].

λ A

=

(\begin{array}{ccc} λ a_{11} & \dots & λ a_{1 n} \\ ⋮ & ⋮ \\ a_{m 1} & \dots & a_{m n} \end{array})

[C].

λ A

=

(\begin{array}{ccc} λ a_{11} & \dots & λ a_{1 n} \\ ⋮ & ⋮ \\ λ a_{m 1} & \dots & λ a_{m n} \end{array})

[D].

λ A

=

(\begin{array}{ccc} \frac{1}{λ} a_{11} & \dots & \frac{1}{λ} a_{1 n} \\ ⋮ & ⋮ \\ \frac{1}{λ} a_{m 1} & \dots & \frac{1}{λ} a_{m n} \end{array})

$λ A$ $=$ ${(λ a_{i j})}_{m \times n}$ $=$ $(\begin{array}{ccc} λ a_{11} & \dots & λ a_{1 n} \\ ⋮ & ⋮ \\ λ a_{m 1} & \dots & λ a_{m n} \end{array})$