To solve this equation, we need to perform the operations on both sides and see if they are equal:
A = [12-23]
B = [2 1 2 3]
C = [-3 1 2 0]
A(B + C) = [12 - 23]([2 1 2 3] + [-3 1 2 0])
First, we need to perform the operation inside the parentheses:
[2 1 2 3] + [-3 1 2 0] = [-1 2 4 3]
Now, we can multiply A by the sum:
[12 - 23]([-1 2 4 3]) = [-12 24 48 36 -23 -46 -92 -69]
Next, we need to calculate AB and AC:
AB = [12-23][2 1 2 3] = [24 12 24 36 -46 -23 -46 -69]
AC = [12-23][-3 1 2 0] = [-36 12 24 0 69 -23 -46 0]
Finally, we add AB and AC:
[24 12 24 36 -46 -23 -46 -69] + [-36 12 24 0 69 -23 -46 0] = [-12 24 48 36 -23 -46 -92 -69]
Therefore, A(B + C) = AB + AC, and the equation is verified.
If A = [12-23], B=[2123] and C=[-3120] verify that A(B+c) = AB+AC
3 answers
given the context, I suspect that A,B,C are all 2x2 matrices.
Try that on for size.
Try that on for size.
Apologies for the confusion. Let's assume A, B, and C are all 2x2 matrices and verify the equation.
A = [12 -23]
B = [2 1]
[2 3]
C = [-3 1]
[2 0]
Now, let's calculate A(B + C):
B + C = [2 1] + [-3 1] = [-1 2]
[4 3]
Multiplying A by (B + C):
A(B + C) = [12 -23]([-1 2]) = [24 - 49]
[-24 -21]
Next, let's calculate AB and AC:
AB = [12 -23][2 1] = [24 - 49]
[20 - 43]
AC = [12 -23][-3 1] = [9 - 35]
[-6 2]
Finally, let's add AB and AC:
AB + AC = [24 - 49] + [9 - 35] = [33 - 84]
[14 - 41]
Hence, A(B + C) is not equal to AB + AC in this case.
A = [12 -23]
B = [2 1]
[2 3]
C = [-3 1]
[2 0]
Now, let's calculate A(B + C):
B + C = [2 1] + [-3 1] = [-1 2]
[4 3]
Multiplying A by (B + C):
A(B + C) = [12 -23]([-1 2]) = [24 - 49]
[-24 -21]
Next, let's calculate AB and AC:
AB = [12 -23][2 1] = [24 - 49]
[20 - 43]
AC = [12 -23][-3 1] = [9 - 35]
[-6 2]
Finally, let's add AB and AC:
AB + AC = [24 - 49] + [9 - 35] = [33 - 84]
[14 - 41]
Hence, A(B + C) is not equal to AB + AC in this case.