Form a 4 by 3 matrix, B, such that
a) bij=i*j b)ij=(-1)^i+j
a) The matrix B can be formed by using the formula bij = i * j.
B = [ 1 2 3
3 4 6
5 6 9
7 8 12 ]
b) The matrix B can be formed by using the formula bij = (-1)^(i+j).
B = [ 1 -1 1
-1 1 -1
1 -1 1
-1 1 -1 ]
a) To form a 4 by 3 matrix B, where each element bij is equal to i*j, we can proceed as follows:
Step 1: Determine the dimensions of the matrix. In this case, it is a 4 by 3 matrix.
Step 2: Write down the values of i and j for each element in the matrix:
i = 1, 2, 3, 4
j = 1, 2, 3
Step 3: Calculate the value of bij for each element by multiplying the corresponding values of i and j. Fill in the matrix accordingly:
B = | 1*1 1*2 1*3 |
| 2*1 2*2 2*3 |
| 3*1 3*2 3*3 |
| 4*1 4*2 4*3 |
B = | 1 2 3 |
| 2 4 6 |
| 3 6 9 |
| 4 8 12 |
So, the 4 by 3 matrix B, where bij = i*j, is:
B = | 1 2 3 |
| 2 4 6 |
| 3 6 9 |
| 4 8 12 |
To form a 4 by 3 matrix, we need to arrange 4 rows and 3 columns of elements.
a) To form matrix B such that bij = i*j, we can follow these steps:
- Start with an empty 4 by 3 matrix B.
- For each element in matrix B(i, j), assign the value of i * j.
Here's the resulting matrix B:
B = [[1, 2, 3],
[2, 4, 6],
[3, 6, 9],
[4, 8, 12]]
b) To form matrix B such that bij = (-1)^(i+j), we can follow these steps:
- Start with an empty 4 by 3 matrix B.
- For each element in matrix B(i, j), assign the value of (-1)^(i + j).
Here's the resulting matrix B:
B = [[1, -1, 1],
[-1, 1, -1],
[1, -1, 1],
[-1, 1, -1]]
In both cases, I used the i index to represent the row number (starting from 1), and the j index to represent the column number (starting from 1).