# Need algebra help with Linear combination of matrices

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### Question Description

DrMath
School: New York University

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

2A + 6B =    12       10

- 6        32

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Anonymous
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