q. If the columns of an m × n matrix A span Rm, then A has a pivot position in e
ID: 3136352 • Letter: Q
Question
q. If the columns of an m × n matrix A span Rm, then A has a pivot position in every row. r. Let A, B be any two invertible n × n matrices. The inverse of the product AB is B-A-1 T F T F T T T T F s· Let A. B be any two n × n matrices. The tranpose of the product AB is BrAT. F t. A matrix transformation Ax = b is a linear transformation. F u. If an n × n matrix A is invertible, then A has n pivot positions. F v If T is a linear transfornation, then T (cu + dv) = cT(u) + dr (v) for all scalars c d and all u, v in the domain of T. T F w. If T is a linear transformation, then T(0) 0 T F x. If an n × n matrix A is invertible, then Ax = 0 has only trivial solution. T F y. If an n × n matrix A is invertible, then Ax-b has an unique solution x-A-lb. T F z. Let u, v, w, and z be vectors in R. Then the set (u, v, w, z) is linearly dependeut.Explanation / Answer
q) If the columns of an m X n matrix A span Rm, then A has a pivot position in every row.
The given statement is true.
r) Let A,B be any two invertible n X n matrices. The inverse of the product AB is B-1A-1.
The given statement is true.
s) Let A,B be any two n X n matrices. The transpose of the product AB is BTAT.
The given statement is true.
t) A matrix transformation Ax = b is a linear transformation.
The given statement is true.
u) If an n X n matrix A is invertible, then A has n pivot positions.
The given statement is true.
v) If T is a linear transformation, then T(cu + dv) = cT(u) + dT(v) for all scalars c,d and all u,v in the domain of T.
The given statement is true.
w) If T is a linear transformation, then T(0) = 0.
The given statement is true.
x) If an n X n matrix A is invertible, then Ax = 0 has only trivial solution.
The given statement is true.
y) If an n X n matrix A is invertible, then Ax = b has an unique solution x = A-1b.
The given statement is true.
z) Let u, v, w and z be vectors in R3. Then the set {u, v, w, z} is linearly dependent.
The given statement is false.
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