Need algebra help with Linear combination of matrices

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Nov 19th, 2015

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First, we multiply each scalar by its  correspond matrix. We multiply -6 by the matrix B (all the elements of B are multiplied by -6). Then we multiply -2 by the matrix C (all the elements of the matrix C are multiplied by -2).

B =   5    0     3      ------------------>   -6B =   -6(5)    -6(0)     -6(3)  ------------------>  -6B =  -30     0      -18

         5   -4     5                                             -6(5)    -6(-4)    -6(5)                                        -30    24     -30


C =  5    3     4    ----------------->   -2C =  -2(5)     -2(3)      -2(4)   -------------------> -2C =  -10    -6    -8

       -5    0     3                                          -2(-5)    -2(0)     -2(3)                                           10     0     -6


Finally, we add the obtained matrices. We add algebraically their corresponding elements like this.

-6B - 2C =  -30    0    -18     +      -10     -6     -8  =    (-30-10)     (0-6)      (-18-8)  =  -40    -6    -26

                   -30   24   -30               10      0     -6        (-30+10)    (24+0)    (-30-6)      -20    24    -36


Final answer:

-6B - 2C =   - 40     - 6       - 26

                    - 20      24      - 36

Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 19th, 2015

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