Studdy Solution
STEP 1
Assumptions1. The matrix is ax matrix with elements4,1, -1, -. The matrix is ax matrix with elements -5,0, -4,33. We are asked to find the product of the matrices and TS
STEP 2
First, let's find the product of the matrices and. The product of two matrices is found by multiplying each element of the first row of the first matrix with each element of the first column of the second matrix and then adding them up. This is repeated for each row of the first matrix and each column of the second matrix.
=[4−11−2]×[−5−40]
STEP 3
Calculate the first element of the product matrix. This is done by multiplying the elements of the first row of with the elements of the first column of and adding them up.
()11=11×11+12×21=×−5+1×−
STEP 4
Calculate the value of the first element of the product matrix.
()11=4×−+1×−4=−20−4=−24
STEP 5
Repeat the process for the remaining elements of the product matrix.
()12=11×12+12×22=4×0+1×3=3()21=21×11+22×21=−1×−5+−2×−4=5+8=13()22=21×12+22×22=−1×0+−2×3=−
STEP 6
The product matrix is then=[−24133−6]
STEP 7
Now, let's find the product of the matrices and.
TS=[−5−403]×[4−11−2]
STEP 8
Calculate the elements of the product matrix TS in the same way as we did for.
(TS)11=11×11+12×21=−5×4+0×−1=−20(TS)12=11×12+12×22=−5×1+0×−2=−5(TS)21=21×11+22×21=−4×4+3×−1=−16−3=−19(TS)22=21×12+22×22=−4×1+3×−2=−4−6=−10
STEP 9
The product matrix TS is thenTS=[−20−19−5−]As we can see, the product matrices and TS are not equal, which shows that multiplication of matrices is not commutative.
=[−24133−6]=[−20−19−5−]=TS
