Important Questions of Matrices Mathematics | Zigya

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11.

If A2 – A + I = 0, then the inverse of A is

  • A + I

  • A

  • A – I

  • A – I

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12.

If a2 + b2 + c2 = -2 and straight f left parenthesis straight x right parenthesis space equals space open vertical bar table row cell 1 plus straight a squared straight x end cell cell left parenthesis 1 plus straight b squared right parenthesis straight x end cell cell left parenthesis 1 plus straight c squared right parenthesis space straight x end cell row cell left parenthesis 1 plus straight a squared right parenthesis straight x end cell cell 1 plus straight b squared straight x end cell cell left parenthesis 1 plus straight c squared right parenthesis space straight x end cell row cell left parenthesis 1 plus straight a squared right parenthesis straight x end cell cell left parenthesis 1 plus straight b squared right parenthesis straight x end cell cell 1 plus straight c squared straight x end cell end table close vertical bar then f(x) is a polynomial of degree

  • 1

  • 0

  • 2

  • 2

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13.

Let A open parentheses table row 0 0 cell negative 1 end cell row 0 cell negative 1 end cell 0 row cell negative 1 end cell 0 0 end table close parentheses. The only correct statement about the matrix A is

  • A is a zero matrix

  • A2 = I

  • A−1 does not exist

  • A−1 does not exist

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14.

Let space equals space open parentheses table row 1 cell negative 1 end cell 1 row 2 1 cell negative 3 end cell row 1 1 1 end table close parentheses space left parenthesis 10 right parenthesis space straight B space equals space open parentheses table row 4 2 2 row cell negative 5 end cell 0 straight alpha row 1 cell negative 2 end cell 3 end table close parentheses.If B is the inverse of matrix A, then α is

  • -2

  • 5

  • -2

  • -2

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15.

The linear system of equations

8x - 3y - 5z = 05x - 8y + 3z = 03x + 5y - 8z = 0

has

  • Only zero solution

  • Only finite number of non-zero solution

  • No non-zero solution

  • Infinitely many non-zero solution


16.

Let P be the set of non-singular matrices of order 3 over R and Q be the set of all orthogonal of matrices of order 3 over R. Then,

  • P is proper subset of Q

  • Q is proper subset of P

  • Neither P is proper subset of Q nor Q is proper subset of P

  • P  Q = ϕ, the void set


17.

Let A = 111011001. Then, for positive integer n, An is

  • 1nn20n2n00n

  • 1nnn + 1201n001

  • 1n2n0nn200n2

  • 1n2n - 10n + 12n200n + 12


18.

Let a, b, c be such that b(a + c)  0.

If aa +1a - 1- bb +1b - 1cc - 1c + 1 + a + 1b + 1c - 1a - 1b - 1c + 1(- 1)n + 2a(- 1)n + 2b(- 1)nc = 0, then the value of n is 

  • any integer

  • zero

  • any even integer

  • any odd integer


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19.

If x, y and z are greater than 1, then the value of

1logxylogxzlogyx1logyzlogzxlogzy1 is

  • logx . logy . logz

  • logx + logy + logz

  • 0

  • 1 - logx . logy . logz


20.

Let A be a 3 x 3 matrix and B be its adjoint matrix. If I B = 64, then A is equal to

  • ± 2

  • ± 4

  • ± 8

  • ± 12


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