Matrix Addition, Subtraction, and Scalar Multiplication Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Compute 3[2−104]−[13−25]3 \begin{bmatrix} 2 & -1 \\ 0 & 4 \end{bmatrix} - \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}.

Solution

  1. 1
    Step 1: Scalar multiply: 3A=[6−3012]3A = \begin{bmatrix} 6 & -3 \\ 0 & 12 \end{bmatrix}.
  2. 2
    Step 2: Subtract: [6−1−3−30−(−2)12−5]=[5−627]\begin{bmatrix} 6-1 & -3-3 \\ 0-(-2) & 12-5 \end{bmatrix} = \begin{bmatrix} 5 & -6 \\ 2 & 7 \end{bmatrix}.
  3. 3
    Check: (3⋅2−1,3⋅(−1)−3,…)=(5,−6,2,7)(3 \cdot 2 - 1, 3 \cdot (-1) - 3, \ldots) = (5, -6, 2, 7) ✓

Answer

[5−627]\begin{bmatrix} 5 & -6 \\ 2 & 7 \end{bmatrix}
Scalar multiplication multiplies every entry by the scalar. Combined with subtraction, this demonstrates that matrix operations follow the same order of operations as regular arithmetic.

About Matrix Addition, Subtraction, and Scalar Multiplication

Matrix addition and subtraction are performed entry by entry on matrices of the same dimensions. Scalar multiplication multiplies every entry of a matrix by a single number (the scalar).

Learn more about Matrix Addition, Subtraction, and Scalar Multiplication →

More Matrix Addition, Subtraction, and Scalar Multiplication Examples

Example 1 easy

Compute [formula].

Example 3 easy

Compute [formula].

Example 4 medium

If [formula] and [formula], find [formula].

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