Answer.AI
Question
Mathematics
Find the product of the following two matrices.
[ 2 5 2 1 0 0 ] [ 0 1 2 1 1 0 0 1 1 ] [[2,-5,2],[],[1,0,0]][[0,1,-2],[],[1,-1,0],[],[0,1,-1]]
order of 1st matrix order of 2 nd matrix
See Answers
Get the Answer.AI App
Solve problem with AI
Best Answer
The order of the first matrix is 2 × 3 2xx3 (2 rows and 3 columns) and the order of the second matrix is 3 × 3 3xx3 (3 rows and 3 columns). Since the number of columns in the first matrix matches the number of rows in the second matrix, we can multiply them using matrix multiplication.
The product of the two matrices is
[ 2 5 2 1 0 0 ] [ 0 1 2 1 1 0 0 1 1 ] = [ 0 9 9 0 1 0 ] [[2,-5,2],[],[1,0,0]][[0,1,-2],[],[1,-1,0],[],[0,1,-1]]=[[0,9,-9],[],[0,1,0]]
To find the product, we multiply the first row of the left matrix by the first column of the right matrix, and so on for each row and column.
Here are the steps of the calculation in more detail:
[ 2 5 2 1 0 0 ] [ 0 1 2 1 1 0 0 1 1 ] = [ ( 2 × 0 ) + ( 5 × 1 ) + ( 2 × 0 ) ( 2 × 1 ) + ( 5 × 1 ) + ( 2 × 1 ) ( 2 × 2 ) + ( 5 × 0 ) + ( 2 × 1 ) ( 1 × 0 ) + ( 0 × 1 ) + ( 0 × 0 ) ( 1 × 1 ) + ( 0 × 1 ) + ( 0 × 1 ) ( 1 × 2 ) + ( 0 × 0 ) + ( 0 × 1 ) ] = [ 0 9 9 0 1 0 ] . {:[[[2,-5,2],[],[1,0,0]][[0,1,-2],[],[1,-1,0],[],[0,1,-1]]],[],[=[[(2xx0)+(-5xx1)+(2xx0),(2xx1)+(-5xx-1)+(2xx1),(2xx-2)+(-5xx0)+(2xx-1)],[],[(1xx0)+(0xx1)+(0xx0),(1xx1)+(0xx-1)+(0xx1),(1xx-2)+(0xx0)+(0xx-1)]]],[],[=[[0,9,-9],[],[0,1,0]].]:}
You might be interested in...
Explore more...
Get the Answer.AI App
Solve problem with AI