Word Count : 434

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Take the four polynomials in $P^3$ and represent each by its coefficient vector with respect to the standard basis $\{1,x,x^2,x^3\}$. Suppose the four polynomials are $$ p_1=1+x- x^2+2x^3,\quad p_2=2-x+x^2+x^3,\quad p_3=3+0\cdot x+2x^2-x^3,\quad p_4=1-2x+0\cdot x^2+0\cdot x^3. $$ Their coefficient matrix (columns are coefficients of $p_1,p_2,p_3,p_4$ from constant term up to $x^3$) is $$ \begin{bmatrix} 1 & 2 & 3 & 1\\[4pt] 1 & -1 & 0 & -2\\[4pt] -1 & 1 & 2 & __________ _____ __________ ______ __________ ____ _________ ____ ____ ____ _______.
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