Posted by **Melissa** on Sunday, January 2, 2011 at 11:12am.

Mark each of the following True or False.

___ a. All vectors in an orthogonal basis have length 1.

___ b. A square matrix is orthogonal if its column vectors are orthogonal.

___ c. If A^T is orthogonal, then A is orthogonal.

___ d. If A is an n*n symmetric orthogonal matrix then A^2=I .

___ e. If A is an n*n symmetric matrix such that A^2=I, then A is orthogonal.

___ f. If A and B are orthogonal n*n matrices, then AB is orthogonal.

___ g. Every orthogonal matrix has nullspace {0}

___ h. Every n*k matrix A has a factorization A=QR, where the column vectors of Q form an orthonormal set and R is an invertible k*k matrix.

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