Download det A

M 340 L
Unique number 53280
QUIZ # 3
LAST NAME (PRINT) ………………………………. First Name …………………..
TRUE
FALSE
1) If A and B are nxn matrices, with detA=2 and detB=3,
then det (A+B) = 5.
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2) det AtA > 0 or = 0
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3) If A3 = 0, then det A = 0.
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4) The null space of A is the solution set of A x = 0 .
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5) The column space of A is the range of the mapping
x  Ax.
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6) The range of a linear transformation is a vector space.
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7) Col A is the set of all solutions of the equation Ax = b.
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8) The column space of a mxn matrix is Rm.
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9) If a finite set S of non zero vectors spans a vector space V
then some subset of S is a basis for V.
10) If B is an echelon form of a matrix A, then the pivot
columns of B form a basis for Col A.
11) If dim V = p, then there exists a spanning set of p+1
vectors in V.
12) If p > or = 2 and dim V = p, then every set of p-1 non
Zero vectors is linearly independent.
13) The dimension of the null space of A is the number of
columns of A that are not pivot columns.
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M 340 L
Unique number 53280
Up to Date PRACTICE QUIZ # 3
LAST NAME (PRINT) ………………………………. First Name …………………..
TRUE
1) det (A+B) = det A + det B
FALSE
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2) If A is invertible (det A )(det A-1 ) = 1.
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3) det At = - det A.
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4) A null space is a vector space.
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5) Nul A is the Kernel of the mapping x  Ax.
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6) The range of a linear transformation is a vector space.
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7) Col A is the set of all vectors that can be written as Ax
for some x.
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8) The Null space of a mxn matrix is Rm.
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9) A basis is a linearly independent set which is as large as
possible.
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10) If B is any echelon form of a matrix A, then the pivot
columns of B form a basis for the column space of A.
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11) If B is any echelon form of a matrix A, then A and B
have the same null space.
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12) If B is obtained from a matrix A by several elementary
row operations, then rank B = rank A.
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13) The pivot columns of A provide a basis of Col A.
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