Find the product, if possible. [8 -7 3][} 9&-8&-7 3&-9&5 -2&-7&-8 ] A. [45-22-115] B. [} 72&56&-21 24&63&15 -16&-16&-24 ] C. [} 45 -22 -115 ] D. [} 8&-7&3 9&-8&-7 3&-9&5 -2&-7&-8 ]

To find the product of the given matrices, we need to multiply the first matrix with the second matrix. <br /><br />The first matrix is a 1x3 matrix, and the second matrix is a 3x3 matrix. <br /><br />To multiply these matrices, we need to perform the dot product of each row of the first matrix with each column of the second matrix.<br /><br />Let's calculate the product step by step:<br /><br />1. Multiply the first row of the first matrix with each column of the second matrix:<br /> - First row, first column: (8 * 9) + (-7 * 3) + (3 * -2) = 72 - 21 - 6 = 45<br /> - First row, second column: (8 * -8) + (-7 * -9) + (3 * -7) = -64 + 63 - 21 = -22<br /> - First row, third column: (8 * -7) + (-7 * 5) + (3 * -8) = -56 - 35 - 24 = -115<br /><br />2. Multiply the second row of the first matrix with each column of the second matrix:<br /> - Second row, first column: (3 * 9) + (-9 * 3) + (5 * -2) = 27 - 27 - 10 = -10<br /> - Second row, second column: (3 * -8) + (-9 * -9) + (5 * -7) = -24 + 81 - 35 = 22<br /> - Second row, third column: (3 * -7) + (-9 * 5) + (5 * -8) = -21 - 45 - 40 = -106<br /><br />3. Multiply the third row of the first matrix with each column of the second matrix:<br /> - Third row, first column: (-2 * 9) + (-7 * 3) + (-8 * -2) = -18 - 21 + 16 = -23<br /> - Third row, second column: (-2 * -8) + (-7 * -9) + (-8 * -7) = 16 + 63 + 56 = 135<br /> - Third row, third column: (-2 * -7) + (-7 * 5) + (-8 * -8) = 14 - 35 + 64 = 43<br /><br />Therefore, the product of the given matrices is:<br />$[\begin{matrix} 45&-22&-115\\ -10&22&-106\\ -23&135&43\end{matrix} ]$<br /><br />So, the correct answer is C. $[\begin{matrix} 45\\ -22\\ -115\end{matrix} ]$