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let U=2i+2j+k/3,V=i-j/√2 & W=-√2(i+j-4k)/6 .compute the scalar products U.V,U.W &V.W . Check whether U,V & W are orthonormal
Comupute all the minors and the cofactors of: [1 2 3]
[2 0 1]
[2 3 4]
Show that if A is a matrix with a row of zeros (or a column of zeros) then A is not invertible
Prove that if A and B are matrices such that A is symmetric, then (BA−1 ) T (A−1BT ) −1 = In.
Suppose V1,V2,VM is linearly independent in V and W€V.Prove that dim span(V1+W1,V2+W,.....VM+W)> or equal to m-1.
2.Suppose U1,U2,.....Um are finite dimensional subspaces of V.Prove that U1+U2+.....Um is finite dimensional and dim(U1+U2+.....Um)<or equal to dim U1+dim U2+.......dim Um.
Prove that if A, B, and C are n × n non-singular matrices, then (ABC)^-1 = C^−1B^−1A^−1 .
Two matrices A and B are equal if
(a) both are rectangular
(b) both have same order
(c) number of columns of A is equal to columns of B
(d) both have same order and equal corresponding elements
choose the correct answer from the multiple choice provided
Find the eigenvalues and eigenvectors of the matrices
1) [ 9 3 ]
2 9
2) 2 0 1
[ 0 2 0 ]
1 0 2
Reduce the quadratic form to a canonical form and find its nature
1) 2xy+2yz+2zx
Assume that T is an n × n matrix with a row of zeros. Prove that T has no inverse.
