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How does scalar multiplication change every entry in a matrix?

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vector parallelogram for addition and subtraction — linear algebra One method of adding and subtracting vectors is to place their tails together and then supply two more sides to form a parallelogram. The vector from their tails to the opposite corner of the parallelogram is equal to the sum of the original vectors. The vector between their heads (starting from the vector being subtracted) is equal to their difference.

In linear algebra, when a matrix $A$ is multiplied by a scalar $c$ , the operation is performed by multiplying every individual element of the matrix by that scalar.1

If $A$ is a matrix with elements $a_{i j}$ (where $i$ denotes the row and $j$ denotes the column), the resulting matrix $c A$ consists of elements equal to $c a_{i j}$ . This process scales every entry in the matrix by the factor $c$ , effectively applying the scalar multiplication to the entire array.1