If `A=[a_(i j)]` is a `3xx3` diagonal matrix such that `a_(11)=1` , `a_(22)=2` and `a_(33)=3` , then find `|A|` .

If A=[a_(i j)] is a 2xx2 matrix such that a_(i j)=i+2j , write A .

If A=[a_(i j)] is a 3xx3 scalar matrix such that a_(11)=2 , then write the value of |A| .

Let A=([a_(i j)])_(3x3) be a matrix such that a_(11)=a_(33)=2 and all the other elements a_(i j)=1 A^(-1)= (a) A^2+5A-I (b) A^2-5A+5I (c) A^2+5A-5I (d) A^2+5A+5I

Let A=[a_(ij)]_(3xx3) be a scalar matrix and a_(11)+a_(22)+a_(33)=15 then write matrix A.

Let A=([a_(i j)])_(3xx3) be a matrix such that AA^T=4Ia n da_(i j)+2c_(i j)=0,w h e r ec_(i j) is the cofactor of a_(i j)a n dI is the unit matrix of order 3. |a_(11)+4a_(12)a_(13)a_(21)a_(22)+4a_(23)a_(31)a_(32)a_(33)+4|+5lambda|a_(11)+1a_(12)a_(13)a_(21)a_(22)+1a_(23)a_(31)a_(32)a_(33)+1|=0 then the value of 10lambda is _______.

Let A=[a_("ij")]_(3xx3) be a matrix such that A A^(T)=4I and a_("ij")+2c_("ij")=0 , where C_("ij") is the cofactor of a_("ij") and I is the unit matrix of order 3. |(a_(11)+4,a_(12),a_(13)),(a_(21),a_(22)+4,a_(23)),(a_(31),a_(32),a_(33)+4)|+5 lambda|(a_(11)+1,a_(12),a_(13)),(a_(21),a_(22)+1,a_(23)),(a_(31),a_(32),a_(33)+1)|=0 then the value of lambda is

Let A=[a_(ij)]_(3xx3) be a square matrix such that A A^(T)=4I, |A| lt 0 . If |(a_(11)+4,a_(12),a_(13)),(a_(21),a_(22)+4,a_(23)),(a_(31),a_(32),a_(33)+4)|=5lambda|A+I|. Then lambda is equal to

Let A be the 2 xx 2 matrix given by A=[a_("ij")] where a_("ij") in {0, 1, 2, 3, 4} such theta a_(11)+a_(12)+a_(21)+a_(22)=4 then which of the following statement(s) is/are true ?

Let A be nxxn matrix given by A=[(a_(11),a_(12),a_(13)……a_(1n)),(a_(21),a_(22),a_(23)…a_(2n)),(vdots, vdots, vdots),(a_(n1),a_(n2),a_(n3).a_("nn"))] Such that each horizontal row is arithmetic progression and each vertical column is a geometrical progression. It is known that each column in geometric progression have the same common ratio. Given that a_(24)=1,a_(42)=1/8 and a_(43)=3/16 Let d_(i) be the common difference of the elements in with row then sum_(i=1)^(n)d_(i) is

a_(1),a_(2),a_(3),a_(4),a_(5), are first five terms of an A.P. such that a_(1) +a_(3) +a_(5) = -12 and a_(1) .a_(2) . a_(3) =8 . Find the first term and the common difference.