If CI=C, find I
C= 2 3
0 1
1 0
C * x = C
x = C/C
C/C = 1
x = 1
I is always all zeros except the main diagonal.
So, here
I =
1 0
0 1
To find the value of I when CI = C, we need to understand that CI represents the matrix multiplication of C and I.
Matrix multiplication is calculated by taking the dot product of each row of the first matrix with each column of the second matrix.
Let's denote C as a 3x2 matrix:
C = [2 3]
[0 1]
[1 0]
And let's denote I as a 2x2 matrix:
I = [a b]
[c d]
To find I, we can set up the matrix equation CI = C and substitute the values of C and I. Then we can solve for a, b, c, and d.
C multiplied by I:
[2 3] [a b] = [2 3]
[0 1] [c d] [0 1]
[1 0] [1 0]
Now, let's perform the matrix multiplication:
The 1st row of C multiplied by the 1st column of I:
2a + 3c = 2
The 1st row of C multiplied by the 2nd column of I:
2b + 3d = 3
The 2nd row of C multiplied by the 1st column of I:
0a + 1c = 0
The 2nd row of C multiplied by the 2nd column of I:
0b + 1d = 1
The 3rd row of C multiplied by the 1st column of I:
1a + 0c = 1
The 3rd row of C multiplied by the 2nd column of I:
1b + 0d = 0
Simplifying these equations, we get:
2a + 3c = 2 (1)
2b + 3d = 3 (2)
c = 0 (3)
b + d = 1 (4)
a = 1 (5)
b = 0 (6)
From equation (5), we find that a = 1.
From equation (3), we find that c = 0.
From equation (6), we find that b = 0.
From equation (4), we find that d = 1.
Therefore, the value of I, when CI = C, is:
I = [1 0]
[0 1]
So, I is a 2x2 identity matrix.