find each sum,difference,or product. If the sum or difference does not exist, write impossible.
if A=[5 2 -7 B=[2 9 -3 C=[-4 2 D=[37 22
-1 0 13 12 4 7 9 7 -5 12
3 8 6] -6 -2 5] 15 33] 11 0]
1.A+B 2.B+C 3.C+D 4.D-B 5.A-B 6.D-C
7.2D 8.4B 9.-3A 10.3C
Your notation is unclear. Please clarify.
For example, does A = 52-7, 5(2-7) or 5^2-7?
Online, "^" is used to indicate an exponent, e.g., x^2 = x squared.
To find the sums, differences, or products of the given matrices, you need to perform the corresponding operations on their corresponding elements. Here's how you can do it:
1. A + B:
You add the corresponding elements from matrices A and B.
Sum of A + B = [5+2 2+9 -7+(-3); -1+12 0+4 13+7; 3+9 8+7 6+(-5)]
= [7 11 -10; 11 4 20; 12 15 1]
2. B + C:
You add the corresponding elements from matrices B and C.
Sum of B + C = [2+(-4) 9+2 -3+(-6); 12+15 4+(-2) 7+5; 9+(-5) 7+12 -2+0]
= [-2 11 -9; 27 2 12; 4 19 -2]
3. C + D:
You add the corresponding elements from matrices C and D.
Sum of C + D = [-4+37 2+22; 2+9 8+7; 15+11 33+0]
= [33 24; 11 15; 26 33]
4. D - B:
You subtract the corresponding elements from matrix B from matrix D.
Difference of D - B = [37-2 22-9; -6-12 -2-4; 15-9 33-7]
= [35 13; -18 -6; 6 26]
5. A - B:
You subtract the corresponding elements from matrix B from matrix A.
Difference of A - B = [5-2 2-9 -7-(-3); -1-12 0-4 13-7; 3-9 8-7 6-(-5)]
= [3 -7 -4; -13 -4 6; -6 1 11]
6. D - C:
You subtract the corresponding elements from matrix C from matrix D.
Difference of D - C = [37-(-4) 22-2; -6-9 -2-7; 15-15 33-33]
= [41 20; -15 -9; 0 0]
7. 2D:
You multiply each element of matrix D by 2.
2D = [2*37 2*22; 2*-6 2*-2; 2*15 2*33]
= [74 44; -12 -4; 30 66]
8. 4B:
You multiply each element of matrix B by 4.
4B = [4*2 4*9; 4*-3 4*-2; 4*12 4*7]
= [8 36; -12 -8; 48 28]
9. -3A:
You multiply each element of matrix A by -3.
-3A = [-3*5 -3*2 -3*(-7); -3*(-1) -3*0 -3*13; -3*3 -3*8 -3*6]
= [-15 -6 21; 3 0 -39; -9 -24 -18]
10. 3C:
You multiply each element of matrix C by 3.
3C = [3*(-4) 3*2; 3*2 3*(-2); 3*15 3*33]
= [-12 6; 6 -6; 45 99]
So, the answers to the given expressions are:
1. A+B = [7 11 -10; 11 4 20; 12 15 1]
2. B+C = [-2 11 -9; 27 2 12; 4 19 -2]
3. C+D = [33 24; 11 15; 26 33]
4. D-B = [35 13; -18 -6; 6 26]
5. A-B = [3 -7 -4; -13 -4 6; -6 1 11]
6. D-C = [41 20; -15 -9; 0 0]
7. 2D = [74 44; -12 -4; 30 66]
8. 4B = [8 36; -12 -8; 48 28]
9. -3A = [-15 -6 21; 3 0 -39; -9 -24 -18]
10. 3C = [-12 6; 6 -6; 45 99]