免费矩阵标量乘法计算器
将矩阵与标量相乘，得到新的矩阵结果。
Ka
3.0000
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.
- 013 × [[1,2],[3,4]] = [[3,6],[9,12]]
- 02Original det = 1×4 - 2×3 = -2
- 03New det = 9 × (-2) = -18 = 3² × (-2)
常见问题
What is scalar multiplication?
Scalar multiplication multiplies every element of a matrix by a single number (the scalar). It scales the entire matrix uniformly.
How does scalar multiplication affect the determinant?
For an n×n matrix, multiplying by scalar k multiplies the determinant by k^n. For a 2×2 matrix, the determinant is multiplied by k².
Is scalar multiplication the same as matrix multiplication?
No, scalar multiplication multiplies every element by a number. Matrix multiplication involves dot products of rows and columns of two matrices.
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