Linear Algebra Answers

Complete { (2, 0, 3)} to form an orthogonal

basis of R³

Given that A= 3 ‐1 2 and B= 4 [‐1 2]

[5 1 7] 5 1 3

I. Evaluate 3A and 2B

ii. 3A‐2B

Given that C= 1 6

[3 9]

4 -3 Evaluate CB

Reduce 2++x²+2x₂x4x−2x4, into canonical form. Find the rank,

index, signature and its nature.

Find an orthonormal basis of R^3 of which (1√10,0,-3/√10) is one element

R^3 is a inner product space over the inner product

<(x1,x2,X3),(y1,y2,y3)> = x1y1+ x2y2 - x3y3

True or false with full explanation

If T: U to V is a one- one linear transformation between finite- dimensional vector space V and W , then T is invertible. True or false with full explanation

Check that T = R^3 to R^3, defined by

T(x1,x2,X3)= (x1+X3, x2+2x3, x1-x2-x3) is a linear operator. Also find the kernel

For any two subspace W1,W2 of R^3 of dimension 2, W1+ W2 is a direct sum . True or false with full explanation

If some eigenvalues of a matrix are repeated, the matrix is not diagonisable.true or false with full explanation

R^3 has infinitely many non zero, proper vector subspaces. True or false with full explanation