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Linear Algebra
Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for b
Linear Algebra
Solve the set of linear equations by Guassian elimination method : a+2b+3c=5, 3a-b+2c=8, 4a-6b-4c=-2. Find c
Linear Algebra
Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for c
Linear Algebra
Let a quadratic form have the expression x2+y2+2z2+2xy+3xz with respect to the
standard basis B1 = f(1;0;0); (0;1;0); (0;0;1)g. Find its expression with respect to the
basis B2 = f(1;1;1); (0;1;0); (0;1;1)g
standard basis B1 = f(1;0;0); (0;1;0); (0;0;1)g. Find its expression with respect to the
basis B2 = f(1;1;1); (0;1;0); (0;1;1)g
Linear Algebra
If A and B are two matrices of same order and rank (A)=rank (B)=n ,
then rank (A+B)=n , for n>=1 .
then rank (A+B)=n , for n>=1 .
Linear Algebra
Let f:C3 to C be defined as f(z)=(z1-z2)-i(2z1+z2+z3), where z=(z1,z2,z3) belongs to C3.
Find aw belongs to C3 such that f(z)=<z,w>, where <,> is the standard inner product on C3.
Find aw belongs to C3 such that f(z)=<z,w>, where <,> is the standard inner product on C3.
Linear Algebra
Let M2(R) be the vector space of all 2*2 matrices over R . Prove that M2(R)=S+T,
where S={A belongs to M2(R)|aij=0, i=1,2} and T={B belongs to M2(R)|bij=0 , i not equal to j} are subspaces of M2(R).
where S={A belongs to M2(R)|aij=0, i=1,2} and T={B belongs to M2(R)|bij=0 , i not equal to j} are subspaces of M2(R).
Linear Algebra
Every singleton subset of
C is a basis of
C
over
C
C is a basis of
C
over
C
Linear Algebra
If V is an eigenvector of an n*n invertible matrix A, then V is also an eigenvector of the matrix A2.
Linear Algebra
If { V1,V2,V3 } is a linearly independent set in R3 , then so is { V1+V2-2V3 , V1-2V2+V3 , -2V1+V2+V3 }.
