Which one of the following statements is NOT TRUE? O a. If H is a p-dimensional subspace of Rn, then a linearly independent set of p vectors in H is a basis for H. O b. The dimension of Nul A is the number of variables in the equation Ax = 0. O c. If B = {V1,..., V p) is a basis for a subspace H and if x = C₁V₁ +...+ Cpvp. then C1₁,..., Cp are the coordinates of x relative to the basis B. O d. The null space of an m x n matrix is a subspace of Rn.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Which one of the following statements is NOT TRUE?
O a. If H is a p-dimensional subspace of R", then a linearly independent set of p vectors in H is a basis for H.
O b. The dimension of Nul A is the number of variables in the equation Ax = 0.
O c. If B = {v1,., V p} is a basis for a subspace H and if x = C1V1 +..+ CpVp. then C1,., Cp are the coordinates of x relative to the basis B.
O d. The null space of an m xn matrix is a subspace of R".
Transcribed Image Text:Which one of the following statements is NOT TRUE? O a. If H is a p-dimensional subspace of R", then a linearly independent set of p vectors in H is a basis for H. O b. The dimension of Nul A is the number of variables in the equation Ax = 0. O c. If B = {v1,., V p} is a basis for a subspace H and if x = C1V1 +..+ CpVp. then C1,., Cp are the coordinates of x relative to the basis B. O d. The null space of an m xn matrix is a subspace of R".
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