Linear Algebra - Study Mode

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[#81] The system of equation, given below, has x + 2y + 4z = 2 4x + 3y + z = 5 3x + 2y + 3z = 1

(A) Unique solution

(B) Two solutions

(C) No solutions

(D) More than two solutions

Correct Answer

(A) Unique solution

[#82] The characteristic equation of a (3 × 3) matrix P is defined as a(λ) = |P - λ$$I$$| = λ 3 + λ 2 + 2λ + 1 = 0 If $$I$$ denotes identity matrix, then the inverse of matrix P will be

(A) (P 2 + P + 2$$I$$)

(B) (P 2 + P + 1)

(C) - (P 2 + P + 1)

(D) - (P 2 + P+ 2$$I$$)

Correct Answer

(D) - (P 2 + P+ 2$$I$$)

[#83] For [{ ext{A}} = left[ {x08egin{array}{*{20}{c}}
1&{ an ,{ ext{x}}} \
{ - an { ext{ x}}}&1
end{array}}
ight],] xa0 xa0 the determinant of A T A -1 is

(A) sec 2 x

(B) cos4x

(C) 1

(D) 0

Correct Answer

(C) 1

[#84] The value of the determinant [left| {x08egin{array}{*{20}{c}}
1&3&2 \
4&1&1 \
2&1&3
end{array}}
ight|] xa0is

(A) -28

(B) -24

(C) -32

(D) 36

Correct Answer

(B) -24

[#85] The value of x 3 obtained by solving following system of linear equation is x 1 + 2x 2 - 2x 3 = 4 2x 1 + x 2 + x 3 = -2 -x 1 + x 2 - x 3 = 2

(A) -12

(B) -2

(C) 0

(D) 12

Correct Answer

(B) -2