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Maths-

General

Easy

Question

If A² = 8A + kI where A = $open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets$ then k is :

7
–7
1
–1

The correct answer is: –7

$open square brackets table attributes columnalign center center columnspacing 1em end attributes row cell 1 comma end cell 0 row cell negative 1 comma end cell 7 end table close square brackets open square brackets table attributes columnalign center center columnspacing 1em end attributes row cell 1 comma end cell 0 row cell negative 1 comma end cell 7 end table close square brackets$ = 8 $open square brackets table row cell 1 comma end cell 0 row cell negative 1 comma end cell 7 end table close square brackets$ + k $open square brackets table row 1 0 row 0 1 end table close square brackets$
or $open square brackets table row cell 1 plus 0 end cell cell 0 plus 0 end cell row cell negative 1 minus 7 end cell cell 0 plus 49 end cell end table close square brackets$ = $open square brackets table row 8 0 row cell negative 8 end cell 56 end table close square brackets$ + $open square brackets table row k 0 row 0 k end table close square brackets$
or $open square brackets table row 1 0 row cell negative 8 end cell 49 end table close square brackets$ = $open square brackets table row cell k plus 8 end cell 0 row cell negative 8 end cell cell k plus 56 end cell end table close square brackets$
$rightwards double arrow$ 1 = k + 8
49 = k + 56
$rightwards double arrow$ k = – 7

Related Questions to study

If A = $open square brackets table row alpha 0 row 1 1 end table close square brackets$ and B = $open square brackets table row 1 0 row 5 1 end table close square brackets$ such that A² = B the $alpha$ n is :

If A = $open square brackets table row alpha 0 row 1 1 end table close square brackets$ and B = $open square brackets table row 1 0 row 5 1 end table close square brackets$ such that A² = B the $alpha$ n is :

Matrix M_r is defined as M_r= $open square brackets table row r cell r – 1 end cell row cell r – 1 end cell r end table close square brackets$ , r $element of$ N. Then det. (M₁) + det.(M₂) + ........... + det.(M₂₀₀₉) = ?

Matrix M_r is defined as M_r= $open square brackets table row r cell r – 1 end cell row cell r – 1 end cell r end table close square brackets$ , r $element of$ N. Then det. (M₁) + det.(M₂) + ........... + det.(M₂₀₀₉) = ?

if $open square brackets table row 1 2 3 row 3 1 2 row 2 3 1 end table close square brackets$ $open square brackets table row x row y row z end table close square brackets$ = $open square brackets table row cell 4 – 2 end cell row cell 0 – 6 end cell row cell – 12 end cell end table close square brackets$ $open square brackets table row 2 row 1 end table close square brackets$ then (x, y, z) is equal to -

if $open square brackets table row 1 2 3 row 3 1 2 row 2 3 1 end table close square brackets$ $open square brackets table row x row y row z end table close square brackets$ = $open square brackets table row cell 4 – 2 end cell row cell 0 – 6 end cell row cell – 12 end cell end table close square brackets$ $open square brackets table row 2 row 1 end table close square brackets$ then (x, y, z) is equal to -

parallel

If A = $open square brackets table row 1 cell 1 divided by 2 end cell row 0 1 end table close square brackets$ then A⁶⁴ is :

If A = $open square brackets table row 1 cell 1 divided by 2 end cell row 0 1 end table close square brackets$ then A⁶⁴ is :

Which of the following is not a disproportionation reaction?
I) $NH subscript 4 NO subscript 3 not stretchy rightwards arrow with straight capital delta on top straight N subscript 2 straight O plus straight H subscript 2 straight O$
II) $straight P subscript 4 not stretchy rightwards arrow with straight capital delta on top PH subscript 3 plus HPO subscript 2 superscript ⊖$
III) $PCl subscript 5 not stretchy rightwards arrow with straight capital delta on top PCl subscript 3 plus Cl subscript 2$
IV) $IO subscript 3 superscript ⊖ plus straight I to the power of ⊖ not stretchy ⟶ straight I subscript 2$

Which of the following is not a disproportionation reaction?
I) $NH subscript 4 NO subscript 3 not stretchy rightwards arrow with straight capital delta on top straight N subscript 2 straight O plus straight H subscript 2 straight O$
II) $straight P subscript 4 not stretchy rightwards arrow with straight capital delta on top PH subscript 3 plus HPO subscript 2 superscript ⊖$
III) $PCl subscript 5 not stretchy rightwards arrow with straight capital delta on top PCl subscript 3 plus Cl subscript 2$
IV) $IO subscript 3 superscript ⊖ plus straight I to the power of ⊖ not stretchy ⟶ straight I subscript 2$

chemistry-General

Which is not true for ozone?

Which is not true for ozone?

chemistry-General

parallel

If A & B are two square matrices such that B = A^–1BA, then (A + B)² equals-

If A & B are two square matrices such that B = A^–1BA, then (A + B)² equals-

If A( $theta$ ) = $open square brackets table row 1 cell tan invisible function application theta end cell row cell negative tan invisible function application theta end cell 1 end table close square brackets$ and AB = I, then (sec² $theta$ ) B is equal to-

If A( $theta$ ) = $open square brackets table row 1 cell tan invisible function application theta end cell row cell negative tan invisible function application theta end cell 1 end table close square brackets$ and AB = I, then (sec² $theta$ ) B is equal to-

If A= $open square brackets table row i cell negative i end cell row cell negative i end cell i end table close square brackets$ , B = $open square brackets table row 1 cell negative 1 end cell row cell negative 1 end cell 1 end table close square brackets$ , then A⁸ equals

If A= $open square brackets table row i cell negative i end cell row cell negative i end cell i end table close square brackets$ , B = $open square brackets table row 1 cell negative 1 end cell row cell negative 1 end cell 1 end table close square brackets$ , then A⁸ equals

parallel

If $open square brackets table row alpha beta row gamma cell negative alpha end cell end table close square brackets$ is square root of I₂, then $alpha comma beta$ and $gamma$ will satisfy the relation-

If $open square brackets table row alpha beta row gamma cell negative alpha end cell end table close square brackets$ is square root of I₂, then $alpha comma beta$ and $gamma$ will satisfy the relation-

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) =

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) =

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 -

parallel

For the matrix A = $open square brackets table row 1 1 0 row 1 2 1 row 2 1 0 end table close square brackets$ , which is correct -

For the matrix A = $open square brackets table row 1 1 0 row 1 2 1 row 2 1 0 end table close square brackets$ , which is correct -

If X = $open square brackets table row 1 1 row 1 1 end table close square brackets$ , then Xⁿ, for n $element of$ N, is equal to -

If X = $open square brackets table row 1 1 row 1 1 end table close square brackets$ , then Xⁿ, for n $element of$ N, is equal to -

If A, B and C are three square matrices of the same size such that B = CAC^–1, then CA³C^–1 is equal to -

If A, B and C are three square matrices of the same size such that B = CAC^–1, then CA³C^–1 is equal to -

parallel

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