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Maths-

General

Easy

Question

If A = $open square brackets table row 4 2 row cell negative 1 end cell 1 end table close square brackets$ , then (A –2I) (A –3I) =

A
I
0
5I

The correct answer is: 0

$open parentheses open square brackets table attributes columnalign center center columnspacing 1em end attributes row 4 2 row cell negative 1 end cell 1 end table close square brackets minus 2 open square brackets table attributes columnalign left left columnspacing 1em end attributes row cell 1 0 end cell row cell 0 1 end cell end table close square brackets close parentheses open parentheses open square brackets table row 4 2 row cell negative 1 end cell 1 end table close square brackets minus 3 open square brackets table row 1 0 row 0 1 end table close square brackets close parentheses$
= $open square brackets table attributes columnalign center center columnspacing 1em end attributes row 2 2 row cell negative 1 end cell cell negative 1 end cell end table close square brackets$ $open square brackets table row 1 2 row cell negative 1 end cell cell negative 2 end cell end table close square brackets$ = $open square brackets table row 0 0 row 0 0 end table close square brackets$ = 0

Related Questions to study

Let A = $open square brackets table row 5 cell 5 alpha end cell alpha row 0 alpha cell 5 alpha end cell row 0 0 5 end table close square brackets$ . If | A² | = 25, then | $alpha$ | equals -

Let A = $open square brackets table row 5 cell 5 alpha end cell alpha row 0 alpha cell 5 alpha end cell row 0 0 5 end table close square brackets$ . If | A² | = 25, then | $alpha$ | equals -

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parallel

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Let a matrix A = $open square brackets table row 1 1 row 0 1 end table close square brackets$ , P = $open square brackets table row cell fraction numerator square root of 3 over denominator 2 end fraction end cell cell fraction numerator 1 over denominator 2 end fraction end cell row cell negative fraction numerator 1 over denominator 2 end fraction end cell cell fraction numerator square root of 3 over denominator 2 end fraction end cell end table close square brackets$ , Q = PAP^T where P^T is transpose of matrix P. then P^T Q²⁰⁰⁵ P is-

parallel

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chemistry-General

parallel

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parallel

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If A^k = 0, for some value of k, (I – A)^p = I + A + A² + …. A^k–1, thus p is (A is nilpotent with index k).

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If the matrix A = $open square brackets table row cell y plus a end cell b c row a cell y plus b end cell c row a b cell y plus c end cell end table close square brackets$ has rank 3, then -

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parallel

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