MATRICES
What is the sum of [3/4 -2/-3]+[-5/3 -4/-2]?
a. [-8/1 2/6]
b. [-2/7 2/-1]
c. [2/-7 6/5]
d. [-2/7 -6/-5]**
What is the difference of [3/4 -2/-3]-[2/7 -5/12]
a. [-3/-1 3/7]
b. [1/-3 3/-15]
c. [-3/3 -3/15]**
d. [-1/3 3/-15]
To find the sum or difference of matrices, you need to add or subtract corresponding entries in the matrices.
Let's go step by step to find the sum and difference of the given matrices.
Given matrices:
Matrix A = [3/4 -2/-3]
Matrix B = [-5/3 -4/-2]
Step 1: Simplify the fractions (if necessary).
The fraction -2/-3 can be simplified to 2/3.
The fraction -4/-2 can be simplified to 2.
So now, we have:
Matrix A = [3/4 2/3]
Matrix B = [-5/3 2]
Step 2: Add or subtract corresponding entries.
To find the sum, we need to add the corresponding entries from both matrices:
Sum = Matrix A + Matrix B
= [3/4 -2/-3] + [-5/3 -4/-2]
= [(3/4) + (-5/3) (2/3) + (2)]
= [9/12 -20/12 4/6 + 12/6]
= [-11/12 -8/6]
= [-11/12 -4/3]
Simplifying further, we get:
Sum = [-11/12 -4/3] = [-11/12 -16/12] = [-27/12]
So, the sum of Matrix A and Matrix B is [-27/12].
Now, let's calculate the difference:
Difference = Matrix A - Matrix B
= [3/4 -2/-3] - [2/7 -5/12]
= [(3/4) - (2/7) (2/3) - (-5/12)]
= [21/28 -8/28 8/12 + 5/12]
= [13/28 13/12]
So, the difference of Matrix A and Matrix B is [13/28 13/12].
Therefore, the correct answer choices are:
Sum: d. [-2/7 -6/-5]
Difference: c. [-3/3 -3/15]