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

1) If are two matrices of order respectively; then their sum is possible.

2) The Matrices are conformable for subtraction.

3) Transpose of a matrix is a matrix.

4) Transpose of a square matrix is a square matrix.

5) A column matrix has many columns and only one row.

Answer:

1) 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.

2) True: Two matrices can be subtracted together if they are of the same order. Here both latex A $ and latex B $ are of the same order.

3) False: The transpose of a matrix is obtained by interchanging rows with columns. Hence the Transpose of a matrix is a matrix.

4) 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.

5) False: A Column matrix has one column and many rows.

Answer:

Question 3: Solve for if;

Answer:

1) 2)

Answer:

1)

2)

1) 2) 3) 4)

Answer:

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

Answer:

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

Question 7: Find from the following equations:

Answer:

Therefore

Therefore

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

1) 2)

Answer:

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

Answer:

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

1) 2)

Answer:

Let

1)

Therefore

Hence

2)

Therefore

Hence

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

1) 2) 3)

Answer:

1)

Therefore

2)

Therefore

3)

Therefore