# Mathematics Questions and Answers – Elementary Operation (Transformation) of a Matrix

«
»

This set of Mathematics Objective Questions & Answers focuses on “Elementary Operation (Transformation) of a Matrix”.

1. How many elementary operations are possible on Matrices?
a) 3
b) 2
c) 6
d) 5

Explanation: There are a total of 6 elementary operations that are possible on matrices, three on rows and three on columns.

2. The following operation is applied on a matrix A=$$\begin{bmatrix}2&3\\6&4\end{bmatrix}$$
R1→R1+R2
Which of the following will be the resulting new matrix?
a) $$\begin{bmatrix}8&7\\6&-4\end{bmatrix}$$
b) $$\begin{bmatrix}8&7\\6&4\end{bmatrix}$$
c) $$\begin{bmatrix}8&7\\6&5\end{bmatrix}$$
d) $$\begin{bmatrix}8&7\\6&2\end{bmatrix}$$

Explanation: Given that, A=$$\begin{bmatrix}2&3\\6&4\end{bmatrix}$$
Applying the elementary operation, R1→R1+R2 we get
B=$$\begin{bmatrix}2+6&3+4\\6&4\end{bmatrix}$$=$$\begin{bmatrix}8&7\\6&4\end{bmatrix}$$.

3. Which of the following matrices will remain same if the elementary operation R1→2R1+3R2 is applied on the matrix?
a) $$\begin{bmatrix}1&2&3\\3&4&1\end{bmatrix}$$
b) $$\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}$$
c) $$\begin{bmatrix}0&1&0\\1&0&1\\0&1&0\end{bmatrix}$$
d) $$\begin{bmatrix}1&0\\1&2\\1&0\end{bmatrix}$$

Explanation: Consider matrix A=$$\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}$$, applying the elementary operation R1→2R1+3R2.
$$\begin{bmatrix}2(0)+3(0)&2(0)+3(0)&2(0)+3(0)\\0&0&0\\0&0&0\end{bmatrix}$$=$$\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}$$.
Therefore, the matrix A=$$\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}$$, remains same after applying the elementary operation.

4. Which of the following is not a valid elementary operation?
a) Ri↔Rj
b) Ri→Rj+kRi
c) Ri→kRi
d) Ri→1+kRi

Explanation: The elementary operation Ri→1+kRiis incorrect, the valid elementary operations on matrices are as follows.
i) Interchanging any two rows and columns
ii) The multiplication of the elements of any row or column by a non-zero number.
iii) The addition to the elements of any row or column, the corresponding elements of any other row and column multiplied by any non-zero number.

5. Which of the following elementary operations has been applied to the matrix A=$$\begin{bmatrix}8&5\\2&8\end{bmatrix}$$ such that the new matrix is $$\begin{bmatrix}12&21\\2&8\end{bmatrix}$$?
a) R1→R1-2R2
b) R1→2R1+R2
c) R1→R2+R1
d) R1→R1+2R2

Explanation: The given matrix is A=$$\begin{bmatrix}8&5\\2&8\end{bmatrix}$$
Applying the elementary operation R1→R1+2R2, we get
$$\begin{bmatrix}8+2(2)&5+2(8)\\2&8\end{bmatrix}$$=$$\begin{bmatrix}12&21\\2&8\end{bmatrix}$$.

6. The following elementary operations are applied to the matrix A=$$\begin{bmatrix}4&5&2\\6&7&1\\3&9&5\end{bmatrix}$$
R1→2R1+3R2
R2→3R2-2R3
Which among the following will be the new matrix?
a) $$\begin{bmatrix}24&31&7\\12&3&7\\3&9&5\end{bmatrix}$$
b) $$\begin{bmatrix}24&31&7\\12&3&-7\\3&9&5\end{bmatrix}$$
c) $$\begin{bmatrix}24&31&7\\6&7&1\\3&9&5\end{bmatrix}$$
d) $$\begin{bmatrix}4&5&2\\6&7&1\\3&9&5\end{bmatrix}$$

Explanation: Given that, A=$$\begin{bmatrix}4&5&2\\6&7&1\\3&9&5\end{bmatrix}$$
Applying row operation, R1→2R1+3R2
⇒$$\begin{bmatrix}2(4)+3(6)&2(5)+3(7)&2(2)+3(1)\\6&7&1\\3&9&5\end{bmatrix}$$=$$\begin{bmatrix}24&31&7\\6&7&1\\3&9&5\end{bmatrix}$$
Applying the row operation, R2→3R2-2R3
⇒$$\begin{bmatrix}24&31&7\\3(6)-2(3)&3(7)-2(9)&3(1)-2(5)\\3&9&5\end{bmatrix}$$=$$\begin{bmatrix}24&31&7\\12&3&-7\\3&9&5\end{bmatrix}$$

7. The new matrix after applying the elementary operation R2→2R2+3R1 on the matrix A=$$\begin{bmatrix}2&5&4\\5&2&6\\7&2&1\end{bmatrix}$$ is _____________
a) $$\begin{bmatrix}2&5&4\\16&19&24\\7&2&1\end{bmatrix}$$
b) $$\begin{bmatrix}2&5&4\\19&19&24\\7&2&1\end{bmatrix}$$
c) $$\begin{bmatrix}2&-5&4\\16&19&24\\7&2&1\end{bmatrix}$$
d) $$\begin{bmatrix}1&5&4\\16&19&24\\7&2&1\end{bmatrix}$$

Explanation: Consider A=$$\begin{bmatrix}2&5&4\\5&2&6\\7&2&1\end{bmatrix}$$, after applying R2→2R2+3R1
⇒$$\begin{bmatrix}2&5&4\\2(5)+3(2)&2(2)+3(5)&2(6)+3(4)\\7&2&1\end{bmatrix}$$=$$\begin{bmatrix}2&5&4\\16&19&24\\7&2&1\end{bmatrix}$$.

8. Which among the following is the new matrix after applying the elementary operation C1→4C1 on the matrix A=$$\begin{bmatrix}5&8\\-1&2\\3&-4\end{bmatrix}$$?
a) $$\begin{bmatrix}5&8\\-1&2\\3&-4\end{bmatrix}$$
b) $$\begin{bmatrix}20&8\\-4&2\\12&-4\end{bmatrix}$$
c) $$\begin{bmatrix}20&8\\4&2\\12&-4\end{bmatrix}$$
d) $$\begin{bmatrix}20&8\\-4&2\\12&4\end{bmatrix}$$

Explanation: Given matrix A=$$\begin{bmatrix}5&8\\-1&2\\3&-4\end{bmatrix}$$ Applying the column operation, C1→4C1 we get
$$\begin{bmatrix}4(5)&8\\4(-1)&2\\4(3)&-4\end{bmatrix}$$=$$\begin{bmatrix}20&8\\-4&2\\12&-4\end{bmatrix}$$

9. The following column matrix operations are applied on a column matrix A=$$\begin{bmatrix}-7&2&6\\-2&3&-5\\2&1&3\end{bmatrix}$$
C2→2C1+C2
C3→3C1+2C3
Which among the following will be the new matrix?
a) $$\begin{bmatrix}-7&-12&6\\2&-1&-5\\2&-5&3\end{bmatrix}$$
b) $$\begin{bmatrix}-7&-12&6\\-2&-1&-5\\2&5&3\end{bmatrix}$$
c) $$\begin{bmatrix}-7&2&6\\-2&3&-5\\2&1&3\end{bmatrix}$$
d) $$\begin{bmatrix}-7&-12&-9\\-2&-1&-16\\2&5&12\end{bmatrix}$$

Explanation: Given that, A=$$\begin{bmatrix}-7&2&6\\-2&3&-5\\2&1&3\end{bmatrix}$$
Applying the column operation, C2→2C1+C2 we get
$$\begin{bmatrix}-7&2(-7)+2&6\\-2&2(-2)+3&-5\\2&2(2)+1&3\end{bmatrix}$$=$$\begin{bmatrix}-7&-12&6\\-2&-1&-5\\2&5&3\end{bmatrix}$$
Applying the column operation, C3→3C1+2C3 we get
$$\begin{bmatrix}-7&-12&2(6)+3(-7)\\-2&-1&2(-5)+3(-2)\\2&5&2(3)+3(2)\end{bmatrix}$$=$$\begin{bmatrix}-7&-12&-9\\-2&-1&-16\\2&5&12\end{bmatrix}$$
Therefore, the resulting new matrix is $$\begin{bmatrix}-7&-12&-9\\-2&-1&-16\\2&5&12\end{bmatrix}$$.

10. Which of the following column operation is incorrect for the matrix A=$$\begin{bmatrix}1&2&5\\6&3&8\end{bmatrix}$$ ?
a) C1→3C1
b) C2→C1+C2
c) C2→2+2C2
d) C2→2C1+2C2-C3