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

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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.
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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) \(\begin{bmatrix}8&7\\6&2\end{bmatrix}\)
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
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) \(\begin{bmatrix}1&0\\1&2\\1&0\end{bmatrix}\)
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.
\(\begin{bmatrix}2(0)+3(0)&2(0)+3(0)&2(0)+3(0)\\0&0&0\\0&0&0\end{bmatrix}\)=\(\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}\).
Therefore, the matrix A=\(\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}\), remains same after applying the elementary operation.
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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
\(\begin{bmatrix}8+2(2)&5+2(8)\\2&8\end{bmatrix}\)=\(\begin{bmatrix}12&21\\2&8\end{bmatrix}\).
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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) \(\begin{bmatrix}4&5&2\\6&7&1\\3&9&5\end{bmatrix}\)
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
⇒\(\begin{bmatrix}2(4)+3(6)&2(5)+3(7)&2(2)+3(1)\\6&7&1\\3&9&5\end{bmatrix}\)=\(\begin{bmatrix}24&31&7\\6&7&1\\3&9&5\end{bmatrix}\)
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) \(\begin{bmatrix}1&5&4\\16&19&24\\7&2&1\end{bmatrix}\)
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
⇒\(\begin{bmatrix}2&5&4\\2(5)+3(2)&2(2)+3(5)&2(6)+3(4)\\7&2&1\end{bmatrix}\)=\(\begin{bmatrix}2&5&4\\16&19&24\\7&2&1\end{bmatrix}\).
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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
\(\begin{bmatrix}4(5)&8\\4(-1)&2\\4(3)&-4\end{bmatrix}\)=\(\begin{bmatrix}20&8\\-4&2\\12&-4\end{bmatrix}\)

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) \(\begin{bmatrix}-7&-12&-9\\-2&-1&-16\\2&5&12\end{bmatrix}\)
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
\(\begin{bmatrix}-7&2(-7)+2&6\\-2&2(-2)+3&-5\\2&2(2)+1&3\end{bmatrix}\)=\(\begin{bmatrix}-7&-12&6\\-2&-1&-5\\2&5&3\end{bmatrix}\)
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 \(\begin{bmatrix}-7&-12&-9\\-2&-1&-16\\2&5&12\end{bmatrix}\).
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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 is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter