Question

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Row matrix	I.	\(\begin{bmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 3\end{bmatrix}\)
B.	Scalar matrix	II.	\(\begin{bmatrix}1\\2\\3\end{bmatrix}\)
C.	Column matrix	III.	\(\begin{bmatrix}1 & 2 & 3\end{bmatrix}\)
D.	Diagonal matrix	IV.	\(\begin{bmatrix}2 & 0 & 0\\0 & 2 & 0\\0 & 0 & 2\end{bmatrix}\)

Choose the correct answer from the options given below:

• A. A - III, B - II, C - I, D - IV
• B. A - III, B - II, C - IV, D - I
• C. A - III, B - IV, C - II, D - I
• D. A - III, B - I, C - IV, D - II

Hint:

Row: 1 by n. Column: n by 1. Scalar: equal diagonal entries.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We match each name of a matrix type with its example by using the basic definitions.

Step 2: Match A.
A row matrix has only one row. \([1\ 2\ 3]\) is such a matrix. So A matches III.

Step 3: Match B.
A scalar matrix is a diagonal matrix with all diagonal entries equal. The matrix with 2, 2, 2 on the diagonal is scalar. So B matches IV.

Step 4: Match C.
A column matrix has only one column. The matrix with entries 1, 2, 3 in a column is such a matrix. So C matches II.

Step 5: Match D.
A diagonal matrix has zeros off the diagonal. The matrix with 1, 2, 3 on the diagonal fits, and its diagonal entries are not all equal. So D matches I.

Step 6: Choose the option.
We get A - III, B - IV, C - II, D - I, which is option 3. The other options mismatch at least one of B, C, D.

Final Answer:
The correct matching is A - III, B - IV, C - II, D - I. \[ \boxed{\text{Option 3}} \]