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Addition and Subtraction of a Matrix

If P is a 2 ×...

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If P is a 2 × 2 matrix such that PT = 3P + I, then tr (P) is equal to

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3 \times 3

matrix such that

P^{T} = 2 P + I

P^{T}

is the transpose of P and I is the

3 \times 3

identify matrix, then there exists a column matrix

X = ⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦ \neq ⎡ ⎢ ⎣ \begin{matrix} 000 \end{matrix} ⎤ ⎥ ⎦

3 \times 3

matrix such that

P^{T} = 2 P + I,

P^{T}

is the transpose of P and I is the

3 \times 3

identity matrix, then there exists a column matrix

X = ⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦ \neq ⎡ ⎢ ⎣ \begin{matrix} 000 \end{matrix} ⎤ ⎥ ⎦

P

3 \times 3

matrix such that

P^{T} = 2 P + I

P^{T}

' is the transpose of

P

I

3 \times 3

identity matrix, then there exists a column matrix

X = ⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦ \neq ⎡ ⎢ ⎣ \begin{matrix} 000 \end{matrix} ⎤ ⎥ ⎦

P

be a non-singular matrix such that

I + P + P^{2} + \dots + P^{n} = O

P^{- 1}

3 \times 3

matrix such that

P^{T} = 2 P + I,

P^{T}

is the transpose of P and I is the

3 \times 3

identity matrix, then there exists a column matrix

X = ⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦ \neq ⎡ ⎢ ⎣ \begin{matrix} 000 \end{matrix} ⎤ ⎥ ⎦

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Addition and Subtraction of a Matrix

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