How to multiply this vectors?

Atrox

Atrox

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I don't know how to multiply vectors if the columns and rows are not the same, any video or anything else would help. Thanks.

(10−2011)⋅(−312042−4−11)\left(\begin{array}{rrr} 1 & 0 & -2 \\ 0 & 1 & 1 \end{array}\right)\cdot\left(\begin{array}{rrr} -3 & 1 & 2 \\ 0 & 4 & 2 \\ -4 & -1 & 1 \end{array}\right)
 
Last edited:
solitude said:
I don't know how to multiply vectors if the columns and rows are not the same, any video or anything else would help. Thanks.

(10−2011)⋅(−312042−4−11)\left(\begin{array}{rrr} 1 & 0 & -2 \\ 0 & 1 & 1 \end{array}\right)\cdot\left(\begin{array}{rrr} -3 & 1 & 2 \\ 0 & 4 & 2 \\ -4 & -1 & 1 \end{array}\right)
Click to expand...
You will get a matrix that is a 2×32\times 3 where the first entry is (1)(−3)+(0)(0)+(0)(0)+(−2)(−4)(1)(-3)+(0)(0)+(0)(0)+(-2)(-4)
and the last entry is (0)(2)+(1)(2)+(1)(1)(0)(2)+(1)(2)+(1)(1)
 
You multiply vectors by computing the dot product, as pka showed. In matrix multiplication you need to compute many dot products.
Show us what you have done and we can inform you if you're right or where you made any mistakes.
 
pka said:
You will get a matrix that is a 2×32\times 3 where the first entry is (1)(−3)+(0)(0)+(0)(0)+(−2)(−4)(1)(-3)+(0)(0)+(0)(0)+(-2)(-4)
and the last entry is (0)(2)+(1)(2)+(1)(1)(0)(2)+(1)(2)+(1)(1)
Click to expand...
why there are two 0's?
 
I can't write vertically.

When you dot V= (a1 a2 a3 ... an) with W = (b1 b2 b3 ... bn) you get a1b1 + a2b2 + a3b3 + a4b4 + ... + anbn

So when you compute (1 0 -2)* (-3 0 -4) = (1)(-3) + (0)(0) + (-2)(-4) = ...
 
I got this result, is it correct?

[532−432]\begin{bmatrix}5&3&2\\-4&3&2\end{bmatrix}
 
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