๐Ÿ“ˆcollege algebra review

key term - Scalar multiple

Definition

A scalar multiple is the result of multiplying a matrix by a scalar (a real number). Each element of the matrix is multiplied by the scalar to produce a new matrix.

5 Must Know Facts For Your Next Test

  1. Multiplying a matrix by a scalar results in each element being scaled by that number.
  2. The operation does not change the dimensions of the original matrix.
  3. Scalar multiplication is distributive, meaning $c(A+B) = cA + cB$ where $c$ is a scalar and $A$, $B$ are matrices.
  4. It is also associative with respect to scalar multiplication, i.e., $(ab)C = a(bC)$ where $a$ and $b$ are scalars and $C$ is a matrix.
  5. If you multiply any matrix by zero, the result is a zero matrix of the same dimensions.

Review Questions

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