Question

Answer each question. What is the product [−574230−166][100010001]\left[ \begin{matrix} 
-5 & 7 & 4 \
2 & 3 & 0 \
-1 & 6 & 6 
\end{matrix} ight]
\quad
\left[ \begin{matrix} 
1 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 1 
\end{matrix} ight]
?

Accepted Answer

Identify the two 3x3 matrices given in the problem. Let's call the first matrix $$ A $$ and the second matrix $$ B . $$Recall that the product of two matrices $$ A $$ and $$ B $$, where both are 3x3, is another 3x3 matrix $$ C = AB . $$Each element $$ c_{ij}  of $$matrix $$ C  is $$found by multiplying the elements of the $$ i -th $$row of $$ A  by $$the corresponding elements of the $$ j -th $$column of $$ B $$ and summing the results. Write the formula for each element $$ c_{ij}  of $$the product matrix $$ C $$:

$$ c_{ij} = a_{i1}b_{1j} + a_{i2}b_{2j} + a_{i3}b_{3j} $$ For each element in the resulting matrix $$ C $$, perform the multiplication and addition as per the formula above. Do this for all rows $$ i = 1, 2, 3 $$ and columns $$ j = 1, 2, 3 . $$After calculating all nine elements $$ c_{ij} $$, arrange them into the 3x3 matrix $$ C $$, which is the product of the two given matrices.

Answer each question. What is the product $[\begin{matrix} - 5 & 7 & 4 \\ 2 & 3 & 0 \\ - 1 & 6 & 6 \end{matrix}]$ ?

Verified video answer for a similar problem:

Key Concepts

Matrix Multiplication

Dimensions and Compatibility

Properties of Matrix Multiplication

Answer each question. What is the product [−574230−166][100010001]\(\left\)[ \(\begin{matrix}\) -5 & 7 & 4 \\2 & 3 & 0 \\-1 & 6 & 6 \(\end{matrix}\) \(\right\)]\(\quad\]\left\)[ \(\begin{matrix}\) 1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \(\end{matrix}\) \(\right\)]?