Matrices, Solved Paper Question: Jee 1 year MATH, Math

Let P be a matrix of order 3 × 3 such that all the entries in P are from the set {–1, 0, 1}. Then, the maximum possible value of the determinant of P is _____ .

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JEE Advanced 2018

Which of the following is(are) NOT the square of a 3 × 3 matrix with real entries?

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JEE Advanced 2017

How many 3 × 3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal entries of M^TM is 5 ?

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JEE Advanced 2017

Let

P = [\begin{matrix} 3 & - 1 & - 2 \\ 2 & 0 & α \\ 3 & - 5 & 0 \end{matrix}]

, where α ∈ ℝ. Suppose Q = [q_ij] is a matrix such that PQ = kI, where k ∈ ℝ, k ≠ 0 and I is the identity matrix of order 3. If

q_{23} = - \frac{k}{8}

and det

(Q) = \frac{k^{2}}{2},

then

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JEE Advanced 2016

Let

P = [\begin{matrix} 1 & 0 & 0 \\ 4 & 1 & 0 \\ 16 & 4 & 1 \end{matrix}]

and I be the identity matrix of order 3. If Q = [q_ij] is a matrix such that P⁵⁰ – Q = I, then

\frac{q_{31} + q_{32}}{q_{21}}

equals

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JEE Advanced 2016

Let X and Y be two arbitrary, 3 ✕ 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 ✕ 3, non-zero, symmetric matrix. Then which of the following matrices is(are) skew symmetric?

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JEE Advanced 2015

If

A = [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ a & 2 & b \end{matrix}]

is a matrix satisfying the equation AA^T = 9I, where I is 3 ✕ 3 identity matrix, then the ordered pair (a, b) is equal to:

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JEE Mains 2015

Let ω be a complex cube root of unity with ω ≠ 1 and P = [p_ij] be a n × n matrix with p_ij = ωⁱ^{+ j}. Then P²≠ 0, when n =

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JEE Advanced 2013

If P is a matrix such that, where is the transpose of P and I is the identity matrix, then there exists a column matrix such that

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JEE Advanced 2012

Let M be a matrix satisfying

and

Then the sum of the diagonal entries of M is

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JEE Advanced 2011

A matrix M is such that M^T + M = 0 where M^T is the transpose of matrix M.
If M =

[\begin{matrix} 2 x & a - 1 & 3 z + 1 \\ 1 - a & y & x + y + z \\ b - 5 & c - 2 & z + 1 \end{matrix}]

then

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JEE Mains 0

If a

2 \times 2

matrix

S_{p} = [\begin{matrix} 1 & p \\ 0 & 1 \end{matrix}]

, where p ∈ N and 4S_p +

(S_{p}^{- 1})

⁴= λ I, where I is unit matrix of order 2, then λ is greater than or equal to

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JEE Advanced 0

Let matrix A =

[\begin{matrix} 3 & 1 \\ 7 & 5 \end{matrix}]

, x and y satisfy A² + xI = yA, where I is the identity matrix. Find

{(x y)}^{\frac{1}{3}}

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JEE Mains 0

Which of the following statement(s) is/are correct ?

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JEE Advanced 0

Let A be a 2 × 2 matrix with non-zero entries. If A²= I, where I is 2 × 2 identity matrix, then trace of A is

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JEE Mains 0

Let A and B be two square matrix of order 3 then which of the following statement(s) is (are) correct ?

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JEE Advanced 0

Let A and B be 3 × 3 non-singular matrices, where A is symmetric, B is skew-symmetric, and (A + B) (A – B) = (A – B) (A + B). If A²B²(A^T B)^–1 (AB^–1)^T = (–1)ⁿ A², then

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JEE Mains 0

If

A^{2} = [\begin{matrix} 25 & 24 \\ 24 & 25 \end{matrix}]

, then matrix A can be

(i)

[\begin{matrix} 4 & 3 \\ 3 & 4 \end{matrix}]

(ii)

[\begin{matrix} - 4 & - 3 \\ - 3 & - 4 \end{matrix}]

(iii)

[\begin{matrix} 4 & - 3 \\ - 3 & 4 \end{matrix}]

(v)

[\begin{matrix} 3 & 4 \\ 4 & 3 \end{matrix}]

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JEE Mains 0

Let

A = [\begin{matrix} 1 & 0 \\ 1 & 1 \end{matrix}]

, then

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JEE Advanced 0

Consider the following statements.
(1) The minimum number of zero's in an skew-symmetric matrix of order n × n is 'n'.
(2) The minimum number of zero's in an upper triangular matrix of order n × n is

\frac{n^{2} - n}{2}

.
(3) The minimum number of zero's in an upper triangular matrix of order n × n is (n² − n).
(4) All the diagonal matrix are a scalar matrix.
Which of the following are correct?

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JEE Mains 0