Form a 4 by 3 matrix, B, such that a) bij= i*j b)=(-1)^i+j

Answer 1

a) To form a matrix B with bij = i*j, we simply need to multiply the row number by the column number for each element of the matrix.

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]

b) To form a matrix B with bij = (-1)^(i+j), we need to alternate signs for each element of the matrix based on the sum of row number (i) and column number (j).

B = [(-1)^(1+1) (-1)^(1+2) (-1)^(1+3)
(-1)^(2+1) (-1)^(2+2) (-1)^(2+3)
(-1)^(3+1) (-1)^(3+2) (-1)^(3+3)
(-1)^(4+1) (-1)^(4+2) (-1)^(4+3)]

B = [1 -1 1
-1 1 -1
1 -1 1
-1 1 -1]

Note: (-1)^0 is equal to 1.