Answer:

If two matrices are equal, their corresponding elements are also equal.

In each case, write the conclusion (if any) that you can draw.

Answer:

(iii) Yes;

Conclusion: Addition of matrices is commutative

(iv) Yes;

Conclusion : Addition of matrices is associative.

Answer:

Answer:

(i) Since, the order of matrix is and that of is is not possible.

(ii) Since, the order of matrix is and that of is also is possible.

Answer:

Answer:

Answer:

Answer:

(ii) No,

(iv) Conclusion: Matrix multiplication is not commutative.

Find the matrix write the conclusion, if any, that you can draw from the result obtained.

Answer:

The result obtained is zero matrix.

Conclusion: The product of two non-zero matrices can be a zero matrix.

Show that Write the conclusion, if any, that you can draw from the result obtained above.

Answer:

From above, we get:

Conclusion :

Matrices and are not equal and matrix is not a zero matrix, even then

Conversely, if it does not imply that That is in we can not cancel matrix from both the sides.

In other words, cancellation law is not applicable in matrix multiplication.

Answer:

Give a reason. If yes, find [ICSE Board 2011]

Answer:

Hence, the number of columns in matrix is same as the number of rows in matrix ; therefore the product is possible.

Answer:

From the results of parts (i) and (ii) it is clear that :

Answer:

Answer:

On solving equations i) and ii), we get a = 2 and c = 5

On solving equations iii) and iv) we get b = 4 and d = 1

Answer:

First of all, we must find the order of matrix .

Let the order of matrix be

Since the product of matrices is possible, only when the number of columns in the first matrix is equal to the number of rows in the second.

Also, the no. of rows of product (resulting) matrix is equal to the no. of rows of first matrix.

On solving the above equations we get and

Write down : (i) the order of the matrix (ii) the matrix .

Answer:

(i) Let the order of matrix

Therefore the order of the matrix

Question 18: State with reason, whether the following are TRUE or FALSE. A, B, C are matrices of order 2 \times 2.

Answer:

(i) FALSE, as matrix multiplication is not commutative

(ii) TRUE, as matrix multiplication is always associative.

(iii) FALSE, as laws of algebra are not applicable to matrices

(iv) TRUE, as in the case of matrices the multiplication is always distributive over addition