Answer:
To solve the given expression 4R, we need to multiply the matrix R by the scalar 4. First, let's define the matrix R as R = [3 7].
To multiply a matrix by a scalar, we simply multiply each element of the matrix by that scalar. In this case, we will multiply each element of R by 4:
4R = 4 * [3 7] = [4*3 4*7] = [12 28].
Therefore, 4R is equal to the matrix [12 28].
Now, let's evaluate the given expression: ( -2 -11 ) * ( 7 11 ) * ( 2 -7 ) * ( 12 7 ) * ( -2 -44 ) * ( 7 28 ) * ( 2 -44 ) * ( 12 28 ) * ( -8 -44 ).
To simplify this expression, we need to perform matrix multiplication from left to right. Matrix multiplication involves multiplying corresponding elements of rows and columns and summing them up.
Let's break down the expression step by step:
Step 1: (-2 -11) * (7 11)
To multiply these matrices, we need to take the dot product of the first row of the first matrix with the first column of the second matrix and sum them up. Similarly, we take the dot product of the second row of the first matrix with the second column of the second matrix and sum them up.
(-2 -11) * (7 11) = (-2*7 + -11*11) = (-14 -121) = [-135].
Step 2: [-135] * (2 -7)
We perform a similar dot product operation as in Step 1.
[-135] * (2 -7) = [-135*2 + -135*-7] = [-270 + 945] = [675].
Step 3: [675] * (12 7)
Again, we perform a dot product operation.
[675] * (12 7) = [675*12 + 675*7] = [8100 + 4725] = [12825].
Step 4: [12825] * (-2 -44)
Dot product operation:
[12825] * (-2 -44) = [12825*-2 + 12825*-44] = [-25650 + -563100] = [-588750].
Step 5: [-588750] * (7 28)
Dot product operation:
[-588750] * (7 28) = [-588750*7 + -588750*28] = [-4121250 + -16485000] = [-20606250].
Step 6: [-20606250] * (2 -44)
Dot product operation:
[-20606250] * (2 -44) = [-20606250*2 + -20606250*-44] = [-41212500 + 906875000] = [865662500].
Step 7: [865662500] * (12 28)
Dot product operation:
[865662500] * (12 28) = [865662500*12 + 865662500*28] = [10387950000 + 24243900000] = [34631850000].
Step 8: [34631850000] * (-8 -44)
Dot product operation:
[34631850000] * (-8 -44) = [34631850000*-8 + 34631850000*-44] = [-277054800000 + -1521449000000] = [-1798503800000].
Therefore, the final result of the given expression is [-1798503800000].
Explanation: