# how to you multiply a 4x4 matrix with a vector 4x1?

4x4 matrix a a vector of [x, y, z, 1]

in java perhaps?

Relevance

| a₁₁ a₁₂ a₁₃ a₁₄ | . . | x | . . | a₁₁x + a₁₂y + a₁₃z + a₁₄ |

| a₂₁ a₂₂ a₂₃ a₂₄ | .*. | y| .= | a₂₁x + a₂₂y + a₂₃z + a₂₄ |

| a₃₁ a₃₂ a₃₃ a₃₄ | . . | z | . . | a₃₁x + a₃₂y + a₃₃z + a₃₄ |

| a₄₁ a₄₂ a₄₃ a₄₄ | . . | 1 | . . | a₄₁x + a₄₂y + a₄₃z + a₄₄ |

If you're coding this in a program, you can do it as follows (sorry, I don't program in java, so I am using Turing):

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First we define a 4x4 array A, variables x, y, z, and a one-dimensional array B with 4 elements. (B will be solution of A x V)

Code should be similar to this:

for i : 1..4

` ` B(i) := A(i,1)*x + A(i,2)*y, A(i,3)*z + A(i,4)

end for

Note: ` ` characters are there just to create spacing. They don't mean anything.

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An alternate method is to keep values of x, y, z, 1 in a one-dimensional array (with 4 elements) named V

Then we can use nested for statements to calculate B:

for i: 1..4

` ` B(i) := 0

` ` for j: 1..4

` ` ` ` B(i) := B(i) + A(i,j)*V(j)

` ` end for

end for