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
View Answer

Answer: c
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=\(\begin{bmatrix}2&3\\6&4\end{bmatrix}\)
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) \(\begin{bmatrix}8&7\\6&2\end{bmatrix}\)
View Answer

Answer: b
Explanation: Given that, A=\(\begin{bmatrix}2&3\\6&4\end{bmatrix}\)
Applying the elementary operation, R1→R1+R2 we get

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) \(\begin{bmatrix}1&0\\1&2\\1&0\end{bmatrix}\)
View Answer

Answer: b
Explanation: Consider matrix A=\(\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}\), applying the elementary operation R1→2R1+3R2.
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
View Answer

Answer: d
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
View Answer

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

6. The following elementary operations are applied to the matrix A=\(\begin{bmatrix}4&5&2\\6&7&1\\3&9&5\end{bmatrix}\)
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) \(\begin{bmatrix}4&5&2\\6&7&1\\3&9&5\end{bmatrix}\)
View Answer

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

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) \(\begin{bmatrix}1&5&4\\16&19&24\\7&2&1\end{bmatrix}\)
View Answer

Answer: a
Explanation: Consider A=\(\begin{bmatrix}2&5&4\\5&2&6\\7&2&1\end{bmatrix}\), after applying R2→2R2+3R1

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) \(\begin{bmatrix}20&8\\-4&2\\12&4\end{bmatrix}\)
View Answer

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

9. The following column matrix operations are applied on a column matrix A=\(\begin{bmatrix}-7&2&6\\-2&3&-5\\2&1&3\end{bmatrix}\)
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) \(\begin{bmatrix}-7&-12&-9\\-2&-1&-16\\2&5&12\end{bmatrix}\)
View Answer

Answer: d
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
Applying the column operation, C3→3C1+2C3 we get
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
View Answer

Answer: c
Explanation: The column operation C2→2+2C2 is incorrect. A non-zero number cannot be directly added to any column or row in a matrix.

Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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