Let three matrices A = $open square brackets table row 2 1 row 4 1 end table close square brackets$ ; B = $open square brackets table row 3 4 row 2 3 end table close square brackets$ and C = $open square brackets table row 3 cell – 4 end cell row cell – 2 end cell 3 end table close square brackets$ then t_r(A) + t_r $open parentheses fraction numerator A B C over denominator 2 end fraction close parentheses$ + t_r $open parentheses fraction numerator A left parenthesis B C right parenthesis to the power of 2 end exponent over denominator 4 end fraction close parentheses$ + t_r $open parentheses fraction numerator A left parenthesis B C right parenthesis to the power of 3 end exponent over denominator 8 end fraction close parentheses$ + ....... + $straight infinity$ =

Let A, B, C, D be (not necessarily square) real matrices such that A^T = BCD; B^T = CDA; C^T = DAB and D^T = ABC for the matrix S = ABCD, consider the two statements.
I. S³ = S
II. S² = S⁴

Let A = $open square brackets table row 1 cell sin invisible function application theta end cell 1 row cell – sin invisible function application theta end cell 1 cell sin invisible function application theta end cell row cell – 1 end cell cell – sin invisible function application theta end cell 1 end table close square brackets$ , where 0 ≤ θ < 2 $pi$ , then

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)

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.

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)

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.

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

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

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

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

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

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

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

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 -

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

The mortality in a town during 4 quarters of a year due to various causes is given below : Based on this data, the percentage increase in mortality in the third quarter is