矩阵标量乘法计算器 — 公式

Scalar Multiplication of a Matrix

Rule

k × [[a, b], [c, d]] = [[ka, kb], [kc, kd]]

Multiply every element by the scalar.

Properties

  • det(kA) = k^n × det(A) for an n×n matrix (k² × det for 2×2)
  • Scalar multiplication distributes over addition: k(A + B) = kA + kB
  • (jk)A = j(kA)

    • 计算示例

    Multiply [[1,2],[3,4]] by scalar 3.

    1. 3 × [[1,2],[3,4]] = [[3,6],[9,12]]
    2. Original det = 1×4 - 2×3 = -2
    3. New det = 9 × (-2) = -18 = 3² × (-2)