Maths-

General

Easy

Question

If A is matrix such that A² + A + 2I = O, then which of the following is INCORRECT ?
(Where I is unit matrix of orde r 2 and O is null matrix of order 2)

A is non-singular
A ≠ O
A is symmetric
A^–1 = $- \frac{1}{2}$ (A+I)

hint Hint:

solve the given expression to check the validity of the inverse of A.

The correct answer is: A is symmetric

A is symmetric is incorrect
A²+ A + 2I = 0
A²+ A= -2I
A+I= A^-1(2I) = A^-1
A^-1= (-1/2)(A+ I)
|A|=0 since A^-1exists., hence it is a non singular matrix.
A= -A^T which means that A is non skew matrix.

inverse of a matrix exists when the determinant of the matrix is 0.
any matrix multiplied by the identity matrix of the same order gives the same matrix.

Identify the incorrect statement in respect of two square matrices A and B conformable for sum and product.

trace of a matrix is the sum of the diagonal elements of a matrix.

Identify the incorrect statement in respect of two square matrices A and B conformable for sum and product.

Maths-General

trace of a matrix is the sum of the diagonal elements of a matrix.

General

chemistry-

In the reaction $3 Br subscript 2 plus 6 CO subscript 3 superscript 2 minus end superscript plus 3 straight H subscript 2 straight O not stretchy rightwards arrow 5 Br to the power of ⊖ plus BrO subscript 3 superscript ⊖ plus 6 HCO subscript 3 superscript ⊖$

chemistry-General

General

Maths-

A is an involutary matrix given by A = $open square brackets table row 0 1 cell – 1 end cell row 4 cell – 3 end cell 4 row 3 cell – 3 end cell 4 end table close square brackets$ then inverse of $fraction numerator A over denominator 2 end fraction$ will be

an involutary matrix is one which follows the property A2= I, I = identity matrix of 3rd order.

A is an involutary matrix given by A = $open square brackets table row 0 1 cell – 1 end cell row 4 cell – 3 end cell 4 row 3 cell – 3 end cell 4 end table close square brackets$ then inverse of $fraction numerator A over denominator 2 end fraction$ will be

Maths-General

an involutary matrix is one which follows the property A2= I, I = identity matrix of 3rd order.

General

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Consider the matrix A, B, C, D with order 2 × 3, 3×4, 4×4, 4×2 respectively. Let x = ( $alpha$ A B $gamma$ C² D)³ where $alpha$ & $gamma$ are scalars . Let |x| = k|ABC²D|³, then k is

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If A³ = O , then I + A + A² equals

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Let A $open square brackets table row 1 2 row 3 4 end table close square brackets$ and B = $open square brackets table row a b row c d end table close square brackets$ are two matrices such that AB = BA and c ≠ 0, then value of $fraction numerator a minus d over denominator 3 b minus c end fraction$ is

Maths-General

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If A and B are two matrices such that AB = B and BA = A, then

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A and B are square matrices and A is non-singular matrix, (A–1BA)n, n $element of$ I⁺, is equal to

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If A = $fraction numerator 1 over denominator 9 end fraction$ $open square brackets table row cell negative 8 end cell 1 4 row 4 4 7 row 1 cell negative 8 end cell 4 end table close square brackets$ then A is -

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Section-wise expenditure of a State Govt. is shown in the given figure. The expenditure incurred on transport is

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The mode of the distribution

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If the mean of the distribution is 2.6, then the value of y is

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The matrix $open square brackets table row 1 omega cell omega to the power of 2 end exponent end cell row omega cell omega to the power of 2 end exponent end cell 1 row cell omega to the power of 2 end exponent end cell 1 omega end table close square brackets$ is a -

maths-General

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If A = $open square brackets table row 1 0 row 1 1 end table close square brackets$ or $open square brackets table row 1 0 row 0 1 end table close square brackets$ , then which of the following holds of all n ≥ 1,

maths-General

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If A is matrix such that A2 + A + 2I = O, then which of the following is INCORRECT ?(Where I is unit matrix of orde r 2 and O is null matrix of order 2)

A is non-singular A ≠ O A is symmetric A–1 = (A+I)

solve the given expression to check the validity of the inverse of A.

The correct answer is: A is symmetric

A is symmetric is incorrectA2+ A + 2I = 0A2+ A= -2IA+I= A-1(2I) = A-1A-1= (-1/2)(A+ I)|A|=0 since A-1 exists., hence it is a non singular matrix.A= -AT which means that A is non skew matrix.

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If A is matrix such that A² + A + 2I = O, then which of the following is INCORRECT ?
(Where I is unit matrix of orde r 2 and O is null matrix of order 2)

A is non-singular
A ≠ O
A is symmetric
A^–1 = $- \frac{1}{2}$ (A+I)

A is symmetric is incorrect
A²+ A + 2I = 0
A²+ A= -2I
A+I= A^-1(2I) = A^-1
A^-1= (-1/2)(A+ I)
|A|=0 since A^-1exists., hence it is a non singular matrix.
A= -A^T which means that A is non skew matrix.

In the reaction $3 Br subscript 2 plus 6 CO subscript 3 superscript 2 minus end superscript plus 3 straight H subscript 2 straight O not stretchy rightwards arrow 5 Br to the power of ⊖ plus BrO subscript 3 superscript ⊖ plus 6 HCO subscript 3 superscript ⊖$

In the reaction $3 Br subscript 2 plus 6 CO subscript 3 superscript 2 minus end superscript plus 3 straight H subscript 2 straight O not stretchy rightwards arrow 5 Br to the power of ⊖ plus BrO subscript 3 superscript ⊖ plus 6 HCO subscript 3 superscript ⊖$

A is an involutary matrix given by A = $open square brackets table row 0 1 cell – 1 end cell row 4 cell – 3 end cell 4 row 3 cell – 3 end cell 4 end table close square brackets$ then inverse of $fraction numerator A over denominator 2 end fraction$ will be

A is an involutary matrix given by A = $open square brackets table row 0 1 cell – 1 end cell row 4 cell – 3 end cell 4 row 3 cell – 3 end cell 4 end table close square brackets$ then inverse of $fraction numerator A over denominator 2 end fraction$ will be

Consider the matrix A, B, C, D with order 2 × 3, 3×4, 4×4, 4×2 respectively. Let x = ( $alpha$ A B $gamma$ C² D)³ where $alpha$ & $gamma$ are scalars . Let |x| = k|ABC²D|³, then k is

Consider the matrix A, B, C, D with order 2 × 3, 3×4, 4×4, 4×2 respectively. Let x = ( $alpha$ A B $gamma$ C² D)³ where $alpha$ & $gamma$ are scalars . Let |x| = k|ABC²D|³, then k is

If A³ = O , then I + A + A² equals

If A³ = O , then I + A + A² equals

A and B are square matrices and A is non-singular matrix, (A–1BA)n, n $element of$ I⁺, is equal to

A and B are square matrices and A is non-singular matrix, (A–1BA)n, n $element of$ I⁺, is equal to

If A = $fraction numerator 1 over denominator 9 end fraction$ $open square brackets table row cell negative 8 end cell 1 4 row 4 4 7 row 1 cell negative 8 end cell 4 end table close square brackets$ then A is -

If A = $fraction numerator 1 over denominator 9 end fraction$ $open square brackets table row cell negative 8 end cell 1 4 row 4 4 7 row 1 cell negative 8 end cell 4 end table close square brackets$ then A is -

The matrix $open square brackets table row 1 omega cell omega to the power of 2 end exponent end cell row omega cell omega to the power of 2 end exponent end cell 1 row cell omega to the power of 2 end exponent end cell 1 omega end table close square brackets$ is a -

The matrix $open square brackets table row 1 omega cell omega to the power of 2 end exponent end cell row omega cell omega to the power of 2 end exponent end cell 1 row cell omega to the power of 2 end exponent end cell 1 omega end table close square brackets$ is a -

If A = $open square brackets table row 1 0 row 1 1 end table close square brackets$ or $open square brackets table row 1 0 row 0 1 end table close square brackets$ , then which of the following holds of all n ≥ 1,

If A = $open square brackets table row 1 0 row 1 1 end table close square brackets$ or $open square brackets table row 1 0 row 0 1 end table close square brackets$ , then which of the following holds of all n ≥ 1,