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AAKASH SERIES-APPENDICES (REVISION EXERCISE)-DETERMINANTS
- If A(K)=[(K,K-1),(K-1,K)] then |A(1)|+|A(2)|+...+|A(2011)|=
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- If f(x)=|(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x)| then f(root(3)(2))=
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- If f(x)=|(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)...
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- |(a-b-c,2b,2c),(2a,b-c-a,2c),(2a,2b,c-a-b)|=
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- |(sin theta, cos theta, sin2theta),(sin(theta+(2pi)/(3)),cos(theta+(2p...
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- |(3, a+b+c, a^(2)+b^(2)+c^(2)),(a+b+c, a^(2)+b^(2)+c^(2), a^(3)+b^(3)+...
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- |(1,a,a^(2)+bc),(1,b,b^(2)+ac),(1,c,c^(2)+ab)|=k(a-b),(b-c), (c-a) the...
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- If A=[(0, 1,0),(0, 0,1),(-c,-b,-a)] then A^(3)+aA^(2)+bA+cI is
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- If bc+ca+ab=18, and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=...
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- If A=((1,2,1),(-1,0,3),(2,-1,1)) then characteristic equation is given...
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- Let A be a 2xx2 matrix with non-zero entries and let A^(2)=I, where I...
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- If alpha, beta ne 0 and f(n)=a^(n)+beta^(n) and |(3,1+f(1),1+f(2)),(1+...
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- If B is a 3xx3 matrix such that B^(2)=0, then det. [(I+B)^(50)-50B]...
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- If |(a^(2), b^(2), c^(2)),((a+lambda)^(2), (b+lambda)^(2), (c+lambda)^...
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- If f(theta)=|(1, cos theta, 1),(-sin theta, 1,-cos theta),(-1,sin thet...
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- If Delta(r )=|(r,2r-1, 3r-2),((n)/(2), n-1, a),((1)/(2)n(n-1), (n-1)^(...
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- If a, b, c are sides of a scalene triangle, then the value of |(a,b,c...
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- Let S={((a(11), a(12)),(a(21), a(22))):a(ij) in {0,1,2},a(11)=a(22)} ...
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- If A is an 3xx3 non-singular matrix such that AA' = A'A and B=A^(-1)A'...
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- The least value of the product xyz for which the determinant |(x,1,1)...
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