Calculadora de Multiplicação Escalar de Matriz

Multiplique uma matriz por um escalar.

Scalar (k)

a (row 1, col 1)

b (row 1, col 2)

c (row 2, col 1)

d (row 2, col 2)

3.0000

Kb6.0000

Kc9.0000

New Det-18.0000

Formula

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

Multiply every element by the scalar.

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)

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

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.

Aprender

Calculate matrix determinants.

Find the matrix inverse.

Calculate dot products.