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Question 1: State True or False. If False, please state the reason.

- If and are two matrices of order and respectively; then their sum is possible.
- The Matrices and are conformable for subtraction.
- Transpose of a matrix is a matrix.
- Transpose of a square matrix is a square matrix.
- A column matrix has many columns and only one row.

Answer:

*False:*Two matrices can be added together if they are of the same order. Here is of the Order while is of the order . Hence they cannot be added.*True:*Two matrices can be subtracted together if they are of the same order. Here both latex A &s=0$ and latex B &s=0$ are of the same order.*False:*The transpose of a matrix is obtained by interchanging rows with columns. Hence the Transpose of a matrix is a matrix.*True:*Yes Transpose of a square matrix is a square matrix. Here the number of rows is equal to the number of columns. Hence even on transposing, the matrix would remain as a square matrix.*False:*A Column matrix has one column and many rows.

Question 2: Given , find .

Answer:

also

Question 3: Solve for if;

Answer:

1) Given ; Therefore

2)

Question 4: If and find

Answer:

1)

2)

Question 5: If find:

Answer:

1)

2)

3)

4)

Question 6: Wherever possible, write each of the following in a single matrix:

Answer:

1)

2)

3) Adding this is is not possible as the order of the metrices are not the same.

Question 7: Find and from the following equations:

Answer:

1)

Therefore

2)

Therefore

Question 8: Given , find its transpose matrix . If possible find:

Answer:

1)

2)

Question 9: Write the additive inverse of matrices A, B and C where and and .

Answer:

Additive Inverse of is

Additive Inverse of is

Additive Inverse of is

Question 10: Given . Find matrix in each of the following:

Answer:

Let

1)

Therefore

Hence

2)

Therefore

Hence

Question 11: Given and . FInd the matrix in each of the following:

Answer:

Let

1)

Therefore

Hence

2)

Therefore

Hence

3)

Therefore

Hence