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Math · Advanced Math
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True or False 1. If u, v are vectors in R and lu v llu llvll, then u and v are orthogonal 2. If p locates a point on a line tin R and if n 0 is normal tot, then any other point x on t must satisfy n .x n. p 3. A binary vector is a vector with two components which are integers modulo 2. 4. The set of solution vectors to the linear system Ax b is a vector space. 6. IfA is an m x n matrix, then Ax 0 has nontrivial solution if and only if n >m. 7. If a row of a matrix A is multiplied by a scalar c, then the rank of the new matrix is the same as the rank ofA. 8. Elementary row operations do not change the rank of a matrix. 9. The inverse of a square matrix can be computed using only elementary row operations. 10. The rank of the product of two matrices is always equal to the smaller of the ranks of the individual matrices. 11. If A is a 2 x matrix and detA 30. then A is invertible 12. Ifu [u1, u2] and v [vi, are vectors in R then the area of the parallelogram with these Vi vectors as adjacent sides is det Lua v2

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