A=[a(ij)](mxxn) is a square matrix if ……...

`A=[a_(ij)]_(mxxn)` is a square matrix if …………

`mltn`

`mgtn`

m=n

None of these

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Statement 1: If A=([a_(i j)])_(nxxn) is such that ( a )_(i j)=a_(j i),AAi ,ja n dA^2=O , then matrix A null matrix. Statement 2: |A|=0.

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_(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 _______.

If matrix A=[a_(ij)]_(3xx) , matrix B=[b_(ij)]_(3xx3) , where a_(ij)+a_(ji)=0 and b_(ij)-b_(ji)=0 AA i , j , then A^(4)*B^(3) is

Let A=[a_("ij")]_(3xx3), B=[b_("ij")]_(3xx3) and C=[c_("ij")]_(3xx3) be any three matrices, where b_("ij")=3^(i-j) a_("ij") and c_("ij")=4^(i-j) b_("ij") . If det. A=2 , then det. (BC) is equal to _______ .

Construct the matrix A = [ a _(ij)] _(3xx3) , where a_(ij) i- j . State whether A is symmetric or skew-symmetric .

If A is a square matrix of order 3 then |kA| = ………………… .

Statement 1: The inverse of singular matrix A=([a_(i j)])_(nxxn),w h e r ea_(i j)=0,igeqji sB=([a i j-1])_(nxxn)dot Statement 2: The inverse of singular square matrix does not exist.

The matrix A given by (a_(ij))_(2 xx 2) if a_(ij) = i - j is ………. .

FULL MARKS-APPLICATIONS OF MATRICES AND DETERMINANTS-ADDITIONAL QUESTIONS SOLVED

Solve the following homogeneous linear equations. x+2y-5z=0,3x+4y+6z...
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For what value of mu the equations. x+y+3z=0,4x+3y+muz=0,2x+y+2z=0 h...
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A=[a(ij)](mxxn) is a square matrix if …………
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Matrices A and B will be inverse of each only if ……………
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If A is an invertible matrix of order 2 thaen det (A)^(-1) is equal to
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Given A=({:(1,-2),(-5,7):}) then A (adj A) =…………..
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The inverse of ({:(2,1),(4,2):}) is ……………
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Given rho(A,B)nerho(A)lt number of unknowns, then the system has. …………...
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Given rho(A,B)nerho(A)lt number of unknowns, then the system has. …………...
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Given rho(A,B)nerho(A)lt number of unknowns, then the system has. …………...
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The rank of the matrix [{:(1,2,3),(2,4,6),(3,6,9):}] is ……………….
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If the rank of the matrix ({:(1,0,-1),(2,5,lamda),(3,6,9):}) is 3, the...
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If A = [2 0 1] then the rank of "AA"^(T) is …………..
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If the rank of the matrix [(lambda,-1,0),(0, lambda,-1),(-1,0,lambda)]...
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If A is a scalar matrix with scalar kne0, of order 3, then A^(-1) is …...
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If A=[{:(2,1),(3,4):}], then (adjA)A………..
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If A is a square matrix of order n, then |adj A|=
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If A is a matrix of order 3, then det (kA) …………….
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If I is the unit matrix of order n, where kne0 is a constant, then adj...
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In a system of 3 linear non-homogeneous equations with three unknowns,...
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