Let A be a matrix of order 2 - 2 such that A2 - O I - A100 -

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Involutory Matrix

Let A be a ma...

Question

Let A be a matrix of order $2 \times 2$ such that $A^{2} = O$
$(I + A)^{100} =$

100 A

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100 (I + A)

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100 I + A

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I + 100 A

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A_{1}, A_{2}, . . ., A_{100}

n (A_{i}) = i + 2,

A_{1} \subset A_{2} \subset A_{3} . . . . . . . . A_{100}

⋂_{i = 3}^{100} A_{i} = A,

n (A) =

A

A^{2} = I .

\frac{A}{2}

I =

The formula for calculating concentration is given by which of the following:

(i) $\frac{m a s s o f s o l u t e}{m a s s o f s o l u t i o n} \times 100$

(ii) $\frac{m a s s o f s o l u t e}{m a s s o f s o l u t e + s o l v e n t} \times 100$

(iii) $\frac{m a s s o f s o l v e n t}{m a s s o f s o l u t i o n} \times 100$

(iv) $\frac{m a s s o f s o l v e n t}{m a s s o f s o l u t e + s o l v e n t} \times 100$

(v) $\frac{m a s s o f s o l u t e}{v o l u m e o f s o l u t i o n} \times 100$

(vi) $\frac{m a s s o f s o l v e n t}{v o l u m e o f s o l u t i o n} \times 100$

A

2 \times 2

A^{2} = 0

A^{2} - (a + d) A + (a d - b c) I

A^{2} - 4 A + 4 I = 0

B = A^{5} - 4 A^{4} + 6 A^{3} + 4 A^{2} + A

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