Important Questions of Matrices Mathematics | Zigya

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 Multiple Choice QuestionsMultiple Choice Questions

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321.

Let A be a 2 × 2 real matrix with entries from {0, 1} and |A|  0. Consider the following two statements;

(P)If A  I2, then |A| = – 1

(Q)If |A| = 1, then tr(A) = 2

where I2 denotes 2 × 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then :

  • (P) is true and (Q) are false

  • Both (P) and (Q) are true

  • Both (P) and (Q) are false

  • (P) is false and (Q) is true


322.

Let A = {x = (x, y, z): PX = 0 and x2 + y2 + z2 = 1}, where 121 - 23 - 419 - 1 P then the set A

  • is a singleton

  • contains more than two elements

  • contains exactly two elements

  • is an empty set.


323.

Let a, b, c  R be all non-zero satisfy a3 + b3 + c3 = 2.If the matrix A = abcbcacab satifies ATA = I, then a value of abc can be :

  • 13

  • - 13

  • 3

  • 23


324.

Let x110 be a 2 × 2 matrix such that A4 = aij2 × 2a11 = 109, then find a22

  • 12

  • 4

  • - 8

  • 10


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 Multiple Choice QuestionsShort Answer Type

325.

If x - 22x - 33x - 42x - 33x - 44x - 53x - 55x - 810x - 17 = Ax3 + Bx2 + Cx + D then find the absolute value B + C = ?


 Multiple Choice QuestionsMultiple Choice Questions

326.

If A =cosθisinθisinθcosθ, θ = π24 and A5 = abcd, where i =  - 1, then which one of the following isnot true ?

  • 0  a2 +b2  1

  • a2 - d2 = 0

  • a2 - b2 = 12

  • a2 - c2 = 1


327.

If a + x = b + y = c + z + 1, where a, b, c, x, y, z are non–zero distinct real numbers then xa + yx + ayb + yy + bzc + yz + c = ?

  • y(a - b)

  • 0

  • y(b - a)

  • y(a - c)


328.

Let m and M be respectively the minimum and maximum value values of cos2x1 + sin2xsin2x1 + cos2xsin2xsin2xcos2xsin2x1 + sin2x

Then the ordered pair (m, M) = ?

  • ( - 3, 3)

  • (1, 3)

  • ( - 3, - 1)

  • ( - 4, - 1)


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