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Linear Algebra
Let V=R^5 find two subspaces U and W such that
U⊕W=R^5
U⊕W=R^5
Linear Algebra
What is the dimension of R^n over R. write it in vectors.?
Linear Algebra
Is there any vector space V such that for no two subspaces U and W
V=U⊕W
Give proper reasoning
V=U⊕W
Give proper reasoning
Linear Algebra
Can all vector in vector space be linearly independent?
Linear Algebra
Is it is possible for vector spaces to have no linearly independent vector?
Linear Algebra
Investigate the nature of the conic 5x2+4xy+2y2+2x+y=1.
Linear Algebra
Find the normal cononial form of the quadratic form 2xy+2yz-x2-y2-z2. Hence compute its signature.
Linear Algebra
Obtain an orthogonal basis with respect to the standard inner product for the subspace for R4 defined by {(X+Y+Z+W)| X+2Y+Z+3W=0 , X-Y-Z=0}.
Linear Algebra
Find the dual basis of the basis e1=(1,1,2) , e2=(1,0,1) , e3=(2,1,0) of the vector R3 over R.
Linear Algebra
Let a quadratic form has expression 6x2+5xy+10y2 with respect to the standard basis of R2. Find its expression with respect to the new basis { (3,1) , (-2,1) } of R2.
