Match List - I with List - II. List I gives 3 × 3 matrices representing 2D transformations and List - II shows the corresponding transformation diagrams.

List I

(Matrix)

List II

(Transformation Diagram)

(A) \(\left[ {\begin{array}{{20}{c}} 2&0&0\\ 0&2&0\\ 0&0&1 \end{array}} \right]\)

(I)

(B) \(\left[ {\begin{array}{{20}{c}} 1&0&2\\ 0&1&2\\ 0&0&1 \end{array}} \right]\)

(II)

(C) \(\left[ {\begin{array}{{20}{c}} {0.5}&{ - 0.866}&0\\ {0.866}&{0.5}&0\\ 0&0&1 \end{array}} \right]\)

(III)

(D) \(\left[ {\begin{array}{{20}{c}} 1&2&0\\ 0&1&0\\ 0&0&1 \end{array}} \right]\)

(IV)

Choose the correct answer from the options given below:

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Match List - I with List - II. List I gives 3 × 3 matrices representing 2D transformations and List - II shows the corresponding transformation diagrams.

List I

(Matrix)

List II

(Transformation Diagram)

(A) \(\left[ {\begin{array}{{20}{c}} 2&0&0\\ 0&2&0\\ 0&0&1 \end{array}} \right]\)

(I)

(B) \(\left[ {\begin{array}{{20}{c}} 1&0&2\\ 0&1&2\\ 0&0&1 \end{array}} \right]\)

(II)

(C) \(\left[ {\begin{array}{{20}{c}} {0.5}&{ - 0.866}&0\\ {0.866}&{0.5}&0\\ 0&0&1 \end{array}} \right]\)

(III)

(D) \(\left[ {\begin{array}{{20}{c}} 1&2&0\\ 0&1&0\\ 0&0&1 \end{array}} \right]\)

(IV)

Choose the correct answer from the options given below:

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UGC NET Computer Science (Paper 2) 2020 Official Paper

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

Answer 1

The correct answer is option 4.

Key Points

\(\left[ {\begin{array}{*{20}{c}} 2&0&0\\ 0&2&0\\ 0&0&1 \end{array}} \right]\) It is the scaling matrix. 2 in x and y-direction by a factor,

Hence A-II is the correct pair.
\(\left[ {\begin{array}{*{20}{c}} 1&0&2\\ 0&1&2\\ 0&0&1 \end{array}} \right]\) is the translation matrix. Vector 2 in each direction of x and y

Hence B-IV is the correct pair
\(\left[ {\begin{array}{*{20}{c}} {0.5}&{ - 0.866}&0\\ {0.866}&{0.5}&0\\ 0&0&1 \end{array}} \right]\)is an angle of 60 degrees rotation matrix.

Hence C-III is the correct pair
\(\left[ {\begin{array}{*{20}{c}} 1&2&0\\ 0&1&0\\ 0&0&1 \end{array}} \right]\)is the shear matrix of quantity 2 with only x-shear.

Hence D-I is the correct pair

∴ Hence the correct answer is A-II, B - IV, C - III, D - I.

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List I (Matrix)	List II (Transformation Diagram)
(A) \(\left[ {\begin{array}{*{20}{c}} 2&0&0\\ 0&2&0\\ 0&0&1 \end{array}} \right]\)	(I)
(B) \(\left[ {\begin{array}{*{20}{c}} 1&0&2\\ 0&1&2\\ 0&0&1 \end{array}} \right]\)	(II)
(C) \(\left[ {\begin{array}{*{20}{c}} {0.5}&{ - 0.866}&0\\ {0.866}&{0.5}&0\\ 0&0&1 \end{array}} \right]\)	(III)
(D) \(\left[ {\begin{array}{*{20}{c}} 1&2&0\\ 0&1&0\\ 0&0&1 \end{array}} \right]\)	(IV)

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