Calculatrice de Multiplication Scalaire Gratuite

Multipliez une matrice par un scalaire. Multipliez chaque élément d'une matrice par un nombre donné.

Ka

3.0000

Kb6.0000
Kc9.0000
New Det-18.0000
Voir la formule →

Formule

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)

    • Exemple Résolu

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

    1. 013 × [[1,2],[3,4]] = [[3,6],[9,12]]
    2. 02Original det = 1×4 - 2×3 = -2
    3. 03New det = 9 × (-2) = -18 = 3² × (-2)

    Questions Fréquentes

    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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