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Question 62Asked in DSSSB TGT Computer Science (Technical), 12 Sep 2025, Shift 2 (1:00 PM)

The normal form of the matrix [ 1 1 0 -2 ]

The normal form of the matrix [ 1 1 0 -2 ] [ 2 0 2 2 ] [ 4 1 3 1 ] is ________.
  1. A[ 1 0 0 0 ] [ 0 1 0 0 ] [ 0 0 0 0 ]
  2. B[ 1 0 0 0 ] [ 0 0 0 0 ] [ 0 0 0 0 ]
  3. C[ 1 0 0 0 ] [ 0 1 0 0 ] [ 0 0 1 0 ]
  4. D[ 1 0 0 0 ] [ 0 1 1 0 ] [ 0 0 1 0 ]
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Correct answer: (A) [ 1 0 0 0 ] [ 0 1 0 0 ] [ 0 0 0 0 ]

Explanation

R2 - 2R1 gives [0, -2, 2, 6] and R3 - 4R1 gives [0, -3, 3, 9], which is 1.5 times the new R2, so one row becomes zero. The rank is 2, so the normal form is [I2 0; 0 0].

From DSSSB TGT Computer Science PYQ (Technical), 12 Sep 2025, Shift 2 (1:00 PM)

This is question 62 of DSSSB TGT Computer Science PYQ (Technical), 12 Sep 2025, Shift 2 (1:00 PM). See all questions of this paper with answers, or attempt the paper as a timed online test to get your score and all-India rank.