## College Algebra (10th Edition)

$\left[\begin{array}{rr} 28 & -9\\ 4 & 23 \end{array}\right]$
A is a 2 by 3 matrix. C is a 3 by 2 matrix. AC is defined and is a 2 by 2 matrix, the entry $[AC]_{ij}$ = (row i of A)$\times$(column j of B) $AC=\left[\begin{array}{lll} 0 & 3 & -5\\ 1 & 2 & 6 \end{array}\right]\left[\begin{array}{ll} 4 & 1\\ 6 & 2\\ -2 & 3 \end{array}\right]$ $=\left[\begin{array}{cc} {0(4)+3(6)+(-5)(-2)}&{0(1)+3(2)+(-5)(3)}\\ {1(4)+2(6)+6(-2)}&{1(1)+2(2)+6(3)}\end{array}\right]$ $=\left[\begin{array}{ll} 0+18+10 & 0+6-15\\ 4+12-12 & 1+4+18 \end{array}\right]$ $=\left[\begin{array}{rr} 28 & -9\\ 4 & 23 \end{array}\right]$