left(
    begin{array}{lll}
    displaystylesum_{i=1}^4x_i^4 & displaystylesum_{i=1}^4x_i^3 & displaystylesum_{i=1}^4x_i^2 \
     & \
    displaystylesum_{i=1}^4x_i^3 & displaystylesum_{i=1}^4x_i^2 & displaystylesum_{i=1}^4x_i \
     & \
    displaystylesum_{i=1}^4x_i^2 & displaystylesum_{i=1}^4x_i   & displaystylesum_{i=1}^4 1
    end{array}
    right)
    left(
    begin{array}{c}
    a \
    b \
    c
    end{array}
    right)
    =
    left(
    begin{array}{l}
    displaystylesum_{i=1}^4x_i^2y_i \
    \
    displaystylesum_{i=1}^4x_iy_i \
    \
    displaystylesum_{i=1}^4y_i
    end{array}
    right)

documentclass{article}
usepackage{mathtools}
newcommandxstrut{vphantom{sumlimits_i^4}}
begin{document}

[
begin{pmatrix}
sumlimits_{i=1}^4 x^4_i & sumlimits_{i=1}^4 x^3_i\
sumlimits_{i=1}^4 x^3_i & sumlimits_{i=1}^4 x^2_i\
sumlimits_{i=1}^4 x^2_i & sumlimits_{i=1}^4 x_i\
end{pmatrix}
begin{pmatrix}
axstrut \ bxstrut \ cxstrut
end{pmatrix}
=
cdots
]

end{document}