If A = (aij ) is a matrix of size 2x3, and if aij = 2i- 3j for all i and j write down A.

A = (aij ) is a matrix of size 2x3, and if aij = 2i- 3j for all i and j write down A.

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****i=1i=2
j=1 -1 +1
j=2 -4 -2
j=3 -7 -5

To write down the matrix A, we need to determine the values of each element aij using the given formula aij = 2i - 3j.

Given that A is a matrix of size 2x3, it means that it has 2 rows and 3 columns.

Let's find the values for each element:

For the first row (i = 1):
- For the first column (j = 1): a11 = 2(1) - 3(1) = 2 - 3 = -1
- For the second column (j = 2): a12 = 2(1) - 3(2) = 2 - 6 = -4
- For the third column (j = 3): a13 = 2(1) - 3(3) = 2 - 9 = -7

For the second row (i = 2):
- For the first column (j = 1): a21 = 2(2) - 3(1) = 4 - 3 = 1
- For the second column (j = 2): a22 = 2(2) - 3(2) = 4 - 6 = -2
- For the third column (j = 3): a23 = 2(2) - 3(3) = 4 - 9 = -5

Now we can write down the matrix A:

A = [ -1 -4 -7 ]
[ 1 -2 -5 ]

Thus, the matrix A is:

A = [ -1 -4 -7 ]
[ 1 -2 -5 ]