Matrices and Determinants 1 Question 2

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2. The total number of matrices A=2xy1 2xy1 (x,yR,xy) for which ATA=3I3 is

======= ####2. The total number of matrices A=[02y12xy12xy1], (x,yR,xy) for which ATA=3I3 is

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed

(2019 Main, 9 April II)

(a) 2

(b) 4

(c) 3

(d) 6

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Answer:

Correct Answer: 2. (b)

Solution:

Given matrix

A=[02y12xy12xy1],(x,yR,xy)

for which

ATA=3I3[02x2x2yyy111][02y12xy12xy1]=[300030003][8x20006y20003]=[300030003]

Here, two matrices are equal, therefore equating the corresponding elements, we get

8x2=3 and 6y2=3x=±38 and y=±12

There are 2 different values of x and y each.

So, 4 matrices are possible such that ATA=3I3.



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