Matrix Addition

Denote the sum of two matrices A and B (of the same dimensions) by C=A+B. The sum is defined by adding entries with the same indices

 c_(ij)=a_(ij)+b_(ij)

over all i and j. For example,

 [a_(11) a_(12); a_(21) a_(22)]+[b_(11) b_(12); b_(21) b_(22)]=[a_(11)+b_(11) a_(12)+b_(12); a_(21)+b_(21) a_(22)+b_(22)].

Matrix addition is therefore both commutative and associative.

Wolfram Web Resources

Mathematica »

The #1 tool for creating Demonstrations and anything technical.

Wolfram|Alpha »

Explore anything with the first computational knowledge engine.

Wolfram Demonstrations Project »

Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.

Computerbasedmath.org »

Join the initiative for modernizing math education.

Online Integral Calculator »

Solve integrals with Wolfram|Alpha.

Step-by-step Solutions »

Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own.

Wolfram Problem Generator »

Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.

Wolfram Education Portal »

Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more.

Wolfram Language »

Knowledge-based programming for everyone.