 # Need algebra help with Linear combination of matrices Anonymous
timer Asked: Nov 19th, 2015
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DrMath
School: New York University   Thank you for the opportunity to help you with your question!

Thank you for the opportunity to help you with your question!

Ok, in order to multiply a given scalar by a matrix we just need to multiply all the elements (or numbers) of the matrix by the given scalar. After this, we cann add the matrices by adding their corresponding elements (first element or number of the first matrix with the first element or number of the second matrix, and so on).

So we would have the following:

A =   6   -7      ----------------->    2A =   2(6)     2(-7)     ----------------->   2A =   12      -14

0    4                                            2(0)      2(4)                                            0         8

B =    0     4     ----------------->   6B =   6(0)      6(4)     ------------------>    6B =    0       24

-1     4                                          6(-1)     6(4)                                            -6      24

Finally, we add the obtained matrices like this:

2A + 6B =   12     -14      +      0       24   =      (12+0)          (-14+24) =   12      10

0        8              -6       24           (0 - 6)           (8 + 24)        -6       32

Final answer:

2A + 6B =    12       10

- 6        32

Please let me know if you need any clarification. I'm always happy to answer your questions.Please let me know if you need any clarification. I'm always happy to answer your questions.

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