Solve the following matrices.(sORRY I DON'T KNOW HOW TO DO THE BRACKETS)
B= 1, -4
-2, 1
3, 0
D= 0, 1
1, 0
G= -3, 1
4, 5
FIND:
a) DG =
b) GD =
c) BG =
d) DD =
e) GG =
haha do it in the calculator, much easier. I have TI 83+, I can do problems like this in the calculator.
heidi - I did the previous one for you. Now you try.
Damon
To solve these matrix operations, we will use the rules of matrix multiplication. Matrix multiplication is only possible when the number of columns in the first matrix is equal to the number of rows in the second matrix.
Let's solve each of the given matrices:
a) DG:
To find the product of two matrices, we multiply each element of the first matrix by the corresponding element in the second matrix and sum up the results.
D = [0, 1; 1, 0]
G = [-3, 1; 4, 5]
The product DG is obtained by multiplying the elements:
First element of DG:
0*(-3) + 1*4 = 4
Second element of DG:
0*1 + 1*5 = 5
Therefore, DG = [4, 5; 4, 5]
b) GD:
G = [-3, 1; 4, 5]
D = [0, 1; 1, 0]
The product GD is obtained by multiplying the elements:
First element of GD:
-3*0 + 1*1 = 1
Second element of GD:
-3*1 + 1*0 = -3
Third element of GD:
4*0 + 5*1 = 5
Fourth element of GD:
4*1 + 5*0 = 4
Therefore, GD = [1, -3; 5, 4]
c) BG:
B = [1, -4; -2, 1; 3, 0]
G = [-3, 1; 4, 5]
To find BG, we need to multiply the elements:
First element of BG:
1*(-3) + (-4)*4 = -3 -16 = -19
Second element of BG:
1*1 + (-4)*5 = 1 - 20 = -19
Third element of BG:
(-2)*(-3) + 1*4 = 6 + 4 = 10
Fourth element of BG:
(-2)*1 + 1*5 = -2 + 5 = 3
Fifth element of BG:
3*(-3) + 0*4 = -9 + 0 = -9
Sixth element of BG:
3*1 + 0*5 = 3 + 0 = 3
Therefore, BG = [-19, -19; 10, 3; -9, 3]
d) DD:
D = [0, 1; 1, 0]
To find DD, we multiply the elements:
First element of DD:
0*0 + 1*1 = 0 + 1 = 1
Second element of DD:
0*1 + 1*0 = 0 + 0 = 0
Third element of DD:
1*0 + 0*1 = 0 + 0 = 0
Fourth element of DD:
1*1 + 0*0 = 1 + 0 = 1
Therefore, DD = [1, 0; 0, 1]
e) GG:
G = [-3, 1; 4, 5]
To find GG, we multiply the elements:
First element of GG:
-3*(-3) + 1*4 = 9 + 4 = 13
Second element of GG:
-3*1 + 1*5 = -3 + 5 = 2
Third element of GG:
4*(-3) + 5*4 = -12 + 20 = 8
Fourth element of GG:
4*1 + 5*5 = 4 + 25 = 29
Therefore, GG = [13, 2; 8, 29]
To summarize:
a) DG = [4, 5; 4, 5]
b) GD = [1, -3; 5, 4]
c) BG = [-19, -19; 10, 3; -9, 3]
d) DD = [1, 0; 0, 1]
e) GG = [13, 2; 8, 29]