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Maths-

General

Easy

Question

Inverse of the matrix $open square brackets table row 3 cell – 2 end cell cell – 1 end cell row cell – 4 end cell 1 cell – 1 end cell row 2 0 1 end table close square brackets$ is

$[\begin{matrix} 1 & 2 & 3 \\ 3 & 3 & 7 \\ - 2 & - 4 & - 5 \end{matrix}]$
$[\begin{matrix} 1 & 2 & 3 \\ 2 & 5 & 7 \\ - 2 & - 4 & - 5 \end{matrix}]$
$[\begin{matrix} 1 & - 3 & 5 \\ 7 & 4 & 6 \\ 4 & 2 & 7 \end{matrix}]$
$[\begin{matrix} 1 & 2 & - 4 \\ 8 & - 4 & - 5 \\ 3 & 5 & 2 \end{matrix}]$

The correct answer is: $open square brackets table row 1 2 3 row 2 5 7 row cell – 2 end cell cell – 4 end cell cell – 5 end cell end table close square brackets$

|A| = $open vertical bar table row 3 cell – 2 end cell cell – 1 end cell row cell – 4 end cell 1 cell – 1 end cell row 2 0 1 end table close vertical bar$
= 3(1) + 2 (– 4 + 2) – 1 (0 – 2)
= 3 – 4 + 2 = 1
adj A = $open square brackets table row 1 2 cell – 2 end cell row 2 5 cell – 4 end cell row 3 7 cell – 5 end cell end table close square brackets to the power of T end exponent$ = $open square brackets table row 1 2 3 row 2 5 7 row cell – 2 end cell cell – 4 end cell cell – 5 end cell end table close square brackets$
A^–1 = $fraction numerator A d j A over denominator vertical line A vertical line end fraction$ = $open square brackets table row 1 2 3 row 2 5 7 row cell – 2 end cell cell – 4 end cell cell – 5 end cell end table close square brackets$

Related Questions to study

If A = $open square brackets table row 2 cell – 1 end cell row cell – 1 end cell 2 end table close square brackets$ and A² – 4A – n I = 0, then n is equal to

If A = $open square brackets table row 2 cell – 1 end cell row cell – 1 end cell 2 end table close square brackets$ and A² – 4A – n I = 0, then n is equal to

The value of x for which the matrix product $open square brackets table attributes columnalign center center center columnspacing 1em end attributes row 2 0 7 row 0 1 0 row 1 cell negative 2 end cell 1 end table close square brackets$ $open square brackets table row cell – x end cell cell 14 x end cell cell 7 x end cell row 0 1 0 row x cell – 4 x end cell cell – 2 x end cell end table close square brackets$ equal an identity matrix is :

The value of x for which the matrix product $open square brackets table attributes columnalign center center center columnspacing 1em end attributes row 2 0 7 row 0 1 0 row 1 cell negative 2 end cell 1 end table close square brackets$ $open square brackets table row cell – x end cell cell 14 x end cell cell 7 x end cell row 0 1 0 row x cell – 4 x end cell cell – 2 x end cell end table close square brackets$ equal an identity matrix is :

If A = $open square brackets table row 1 2 row 3 5 end table close square brackets$ , then A^–1 is equal to :

If A = $open square brackets table row 1 2 row 3 5 end table close square brackets$ , then A^–1 is equal to :

parallel

If A is a singular matrix, then adj A is :

If A is a singular matrix, then adj A is :

Statement - I The value of x for which (sin x + cos x)^{1 + sin 2x} = 2, when 0 ≤ x ≤ , is $straight pi divided by 4$ only.
Statement - II The maximum value of sin x + cos x occurs when x = $straight pi divided by 4$

Statement - I The value of x for which (sin x + cos x)^{1 + sin 2x} = 2, when 0 ≤ x ≤ , is $straight pi divided by 4$ only.
Statement - II The maximum value of sin x + cos x occurs when x = $straight pi divided by 4$

If [1 2 3 ]A = [4 5], the order of matrix A is :

If [1 2 3 ]A = [4 5], the order of matrix A is :

parallel

Let A and B be 3 × 3 matrices, then AB = O implies:

Let A and B be 3 × 3 matrices, then AB = O implies:

If A = $open square brackets table row 1 2 row 3 cell negative 5 end cell end table close square brackets$ , B = $open square brackets table row 1 0 row 0 2 end table close square brackets$ and X is a matrix such that A = B X. Then X equals

If A = $open square brackets table row 1 2 row 3 cell negative 5 end cell end table close square brackets$ , B = $open square brackets table row 1 0 row 0 2 end table close square brackets$ and X is a matrix such that A = B X. Then X equals

If k $open square brackets table row cell negative 1 end cell 2 2 row 2 cell negative 1 end cell 2 row 2 2 cell negative 1 end cell end table close square brackets$ is an orthogonal matrix then k is equal to

If k $open square brackets table row cell negative 1 end cell 2 2 row 2 cell negative 1 end cell 2 row 2 2 cell negative 1 end cell end table close square brackets$ is an orthogonal matrix then k is equal to

parallel

If f(α) = $open square brackets table row cell cos invisible function application alpha end cell cell sin invisible function application alpha end cell row cell negative sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close square brackets$ and $alpha comma beta comma gamma$ are angles of triangle then f( $alpha$ ). f( $beta$ ).f ( $gamma$ ) =

If f(α) = $open square brackets table row cell cos invisible function application alpha end cell cell sin invisible function application alpha end cell row cell negative sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close square brackets$ and $alpha comma beta comma gamma$ are angles of triangle then f( $alpha$ ). f( $beta$ ).f ( $gamma$ ) =

If A is idempotent and A + B = I, then which of the following true?

If A is idempotent and A + B = I, then which of the following true?

Which of the following is not a disporportionation reaction?

Which of the following is not a disporportionation reaction?

chemistry-General

parallel

If f( $alpha$ ) = $open square brackets table row cell cos invisible function application alpha end cell cell negative sin invisible function application alpha end cell 0 row cell sin invisible function application alpha end cell cell cos invisible function application alpha end cell 0 row 0 0 1 end table close square brackets$ , then $open square brackets f left parenthesis alpha right parenthesis close square brackets to the power of negative 1 end exponent$ =

If f( $alpha$ ) = $open square brackets table row cell cos invisible function application alpha end cell cell negative sin invisible function application alpha end cell 0 row cell sin invisible function application alpha end cell cell cos invisible function application alpha end cell 0 row 0 0 1 end table close square brackets$ , then $open square brackets f left parenthesis alpha right parenthesis close square brackets to the power of negative 1 end exponent$ =

If A = $open square brackets table row 0 1 2 row 1 2 3 row 3 a 1 end table close square brackets$ and A^–1 = $open square brackets table row cell 1 divided by 2 end cell cell negative 1 divided by 2 end cell cell 1 divided by 2 end cell row cell negative 4 end cell 3 c row cell 5 divided by 2 end cell cell negative 3 divided by 2 end cell cell 1 divided by 2 end cell end table close square brackets$ then value of a and c is -

If A = $open square brackets table row 0 1 2 row 1 2 3 row 3 a 1 end table close square brackets$ and A^–1 = $open square brackets table row cell 1 divided by 2 end cell cell negative 1 divided by 2 end cell cell 1 divided by 2 end cell row cell negative 4 end cell 3 c row cell 5 divided by 2 end cell cell negative 3 divided by 2 end cell cell 1 divided by 2 end cell end table close square brackets$ then value of a and c is -

A skew symmetric matrix S satisfies the relation S² + I = 0, where I is a unit matrix, then SS´ is -

A skew symmetric matrix S satisfies the relation S² + I = 0, where I is a unit matrix, then SS´ is -

parallel

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