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Maths-

General

Easy

Question

If a, b, $c$ , are real numbers, and $D equals open vertical bar table row a cell 1 plus 2 i end cell cell 3 minus 5 i end cell row cell 1 minus 2 i end cell b cell negative 7 minus 3 i end cell row cell 3 plus 5 i end cell cell negative 7 plus 3 i end cell c end table close vertical bar$ then D is

purely real
purely imaginary
non real
integer

The correct answer is: purely real

Related Questions to study

The value of $lambda$ for which the system ofequations 2x-y-z=12, x-2y+z=-4, x+y+λz=4 has no solution is

Hence λ=−2 for no solution.

The value of $lambda$ for which the system ofequations 2x-y-z=12, x-2y+z=-4, x+y+λz=4 has no solution is

Hence λ=−2 for no solution.

The number of values of $k$ for which the linear equations 4x+ky+2z=0 kx+4y+z=0 2x+2y+z=0 possess a non‐zero solution is :‐

The number of values of $k$ for which the linear equations 4x+ky+2z=0 kx+4y+z=0 2x+2y+z=0 possess a non‐zero solution is :‐

If $a subscript 1 end subscript comma$ $a subscript 2 end subscript comma horizontal ellipsis horizontal ellipsis. a subscript n end subscript comma$ $a subscript n plus 1 end subscript$ are in $G P blank a n d blank a subscript i end subscript greater than 0 for all i comma$ then $open vertical bar table row cell l o g invisible function application a subscript n end subscript end cell cell l o g invisible function application a subscript n plus 2 end subscript end cell cell l o g invisible function application a subscript n plus 4 end subscript end cell row cell l o g invisible function application a subscript n plus 6 end subscript end cell cell l o g invisible function application a subscript n plus 8 end subscript end cell cell l o g invisible function application a subscript n plus 10 end subscript end cell row cell l o g invisible function application a subscript n plus 12 end subscript end cell cell l o g invisible function application a subscript n plus 14 end subscript end cell cell l o g invisible function application a subscript n plus 16 end subscript end cell end table close vertical bar$ is equal to

If $a subscript 1 end subscript comma$ $a subscript 2 end subscript comma horizontal ellipsis horizontal ellipsis. a subscript n end subscript comma$ $a subscript n plus 1 end subscript$ are in $G P blank a n d blank a subscript i end subscript greater than 0 for all i comma$ then $open vertical bar table row cell l o g invisible function application a subscript n end subscript end cell cell l o g invisible function application a subscript n plus 2 end subscript end cell cell l o g invisible function application a subscript n plus 4 end subscript end cell row cell l o g invisible function application a subscript n plus 6 end subscript end cell cell l o g invisible function application a subscript n plus 8 end subscript end cell cell l o g invisible function application a subscript n plus 10 end subscript end cell row cell l o g invisible function application a subscript n plus 12 end subscript end cell cell l o g invisible function application a subscript n plus 14 end subscript end cell cell l o g invisible function application a subscript n plus 16 end subscript end cell end table close vertical bar$ is equal to

parallel

If $a comma$ $b comma$ $c$ are real then the value of determinant $open vertical bar table row cell a to the power of 2 end exponent plus 1 end cell cell a b end cell cell a c end cell row cell a b end cell cell b to the power of 2 end exponent plus 1 end cell cell b c end cell row cell a c end cell cell b c end cell cell c to the power of 2 end exponent plus 1 end cell end table close vertical bar equals 1$ if

If $a comma$ $b comma$ $c$ are real then the value of determinant $open vertical bar table row cell a to the power of 2 end exponent plus 1 end cell cell a b end cell cell a c end cell row cell a b end cell cell b to the power of 2 end exponent plus 1 end cell cell b c end cell row cell a c end cell cell b c end cell cell c to the power of 2 end exponent plus 1 end cell end table close vertical bar equals 1$ if

The system of linear equations x+y-z=6, x+2y-3z=14 and $2 x plus 5 y minus lambda z equals 9 left parenthesis lambda element of R right parenthesis$ has a unique solution if

Hence option B is the correct option

The system of linear equations x+y-z=6, x+2y-3z=14 and $2 x plus 5 y minus lambda z equals 9 left parenthesis lambda element of R right parenthesis$ has a unique solution if

Hence option B is the correct option

If $D equals$ $open vertical bar table row cell a to the power of 2 end exponent plus 1 end cell cell a b end cell cell a c end cell row cell b a end cell cell b to the power of 2 end exponent plus 1 end cell cell b c end cell row cell c a end cell cell c b end cell cell c to the power of 2 end exponent plus 1 end cell end table close vertical bar$ then $D equals$

If $D equals$ $open vertical bar table row cell a to the power of 2 end exponent plus 1 end cell cell a b end cell cell a c end cell row cell b a end cell cell b to the power of 2 end exponent plus 1 end cell cell b c end cell row cell c a end cell cell c b end cell cell c to the power of 2 end exponent plus 1 end cell end table close vertical bar$ then $D equals$

parallel

Let $A equals open curly brackets table attributes columnalign left end attributes row cell c o s to the power of negative 1 end exponent x end cell cell c o s to the power of negative 1 end exponent y end cell cell c o s to the power of negative 1 end exponent end cell z row cell c o s to the power of negative 1 end exponent y end cell cell c o s to the power of negative 1 end exponent z end cell cell c o s to the power of negative 1 end exponent x end cell blank row cell c o s to the power of negative 1 end exponent z end cell cell c o s to the power of negative 1 end exponent x end cell cell c o s to the power of negative 1 end exponent y end cell blank end table close curly brackets$ such that $vertical line A vertical line equals 0$ , then maximum value of $x plus y plus z$ is

Let $A equals open curly brackets table attributes columnalign left end attributes row cell c o s to the power of negative 1 end exponent x end cell cell c o s to the power of negative 1 end exponent y end cell cell c o s to the power of negative 1 end exponent end cell z row cell c o s to the power of negative 1 end exponent y end cell cell c o s to the power of negative 1 end exponent z end cell cell c o s to the power of negative 1 end exponent x end cell blank row cell c o s to the power of negative 1 end exponent z end cell cell c o s to the power of negative 1 end exponent x end cell cell c o s to the power of negative 1 end exponent y end cell blank end table close curly brackets$ such that $vertical line A vertical line equals 0$ , then maximum value of $x plus y plus z$ is

Statement‐I : The inverse of the matrix $A equals left square bracket a subscript i j end subscript right square bracket subscript n cross times n end subscript$ where $a subscript i j end subscript equals 0 comma$ $i greater or equal than j$ is $B equals left square bracket a subscript i j to the power of negative 1 end exponent end subscript right square bracket subscript n cross times n end subscript$
Statement‐II : The inverse of singular matrix does not exist.

Hence option D is the suitable option

Statement‐I : The inverse of the matrix $A equals left square bracket a subscript i j end subscript right square bracket subscript n cross times n end subscript$ where $a subscript i j end subscript equals 0 comma$ $i greater or equal than j$ is $B equals left square bracket a subscript i j to the power of negative 1 end exponent end subscript right square bracket subscript n cross times n end subscript$
Statement‐II : The inverse of singular matrix does not exist.

Hence option D is the suitable option

Let $P equals open square brackets a subscript i j end subscript close square brackets$ be a $3 cross times 3$ matrix and let $Q equals left square bracket b subscript i j end subscript right square bracket$ , where $b subscript i j end subscript equals 2 to the power of i plus j end exponent a subscript i j end subscript$ for $1 less than i comma$ $j less than 3$ If the determinant of $P$ is 2, then the determinant of the matrix $Q$ is ‐

Let $P equals open square brackets a subscript i j end subscript close square brackets$ be a $3 cross times 3$ matrix and let $Q equals left square bracket b subscript i j end subscript right square bracket$ , where $b subscript i j end subscript equals 2 to the power of i plus j end exponent a subscript i j end subscript$ for $1 less than i comma$ $j less than 3$ If the determinant of $P$ is 2, then the determinant of the matrix $Q$ is ‐

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