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