JEE Main 2017 · 9 Apr · Shift 1 · Mathematics Q64

MathematicsSingle correct+4 / -1Question 64 of 90

For two 3 × 3 matrices A and B, let $A+B=2B'$ and $3A+2B=I_3$ , where B′ is the transpose of B and $I_3$ is 3 × 3 identity matrix. Then :

5A+10B=2I_3

10A+5B=3I_3

B+2A=I_3

3A+6B=2I_3

Answer and worked solution

Official answer: B

From $A=2B'-B$ , $3A+2B=6B'-B=I$ . Transposing, $6B-B'=I$ , so $B'=6B-I$ and $36B-6I-B=I$ : $B=\frac I5$ . Then $A=\frac I5$ too, and $10A+5B=3I_3$ .

JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 64