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: Look at shapes first.
Row and column matrices are decided by shape alone. The only 1 by 3 array is III, so A is III. The only 3 by 1 array is II, so C is II.

Step 2: Two square matrices left.
The two 3 by 3 matrices are I and IV. Both have zeros outside the main diagonal, so both are diagonal matrices.

Step 3: Separate scalar from general diagonal.
The matrix IV has the same number 2 on all diagonal places, so it is scalar. The matrix I has 1, 2, 3, so it is diagonal but not scalar. This gives B - IV and D - I.

Step 4: Combine.
A - III, B - IV, C - II, D - I is option 3.

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