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35 Cards in this Set
- Front
- Back
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if H is a p-dimensional subspace of R^n , then a linearly independent set of p vectors in H is a basis for H
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T
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a null space is a vector space
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t
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The dimension of Col A is the number of pivot columns in A
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T
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The determinant of a triangular matrix is the sum of the entries on the main diagonal
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F
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detAt = -1det A
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F
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det(A+B)=det A + det B
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F
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a row replacement operation does not affect the determinant of a matrix
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T
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a single vector by itself is linearly dependent
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F
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the column space of an m x n matrix is in R^m
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T
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R2 is a subspace of R3
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F
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To be a subspace?
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1. must contain the zero vector
2. close under addition 3. closed under scalar mult |
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A is invertible if and only if ..
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det A <> 0
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det AB =
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det A det B
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Det A^t
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Det A
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row interchange
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-1
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row scaling
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pull it out
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det A^-1
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1/detA
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1
9 is in a subspace H with a basis where b1 is 1 -5 b2 is -2 3 find the B coordinate vector |
-3
-2 |
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o 5 1
4 -3 0 2 4 1 down second col |
2
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let A and B be 3 x 3 matrices, with det A = 4 and det B = -3
compute det(2AB) |
f
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compute det B^5
1 0 1 1 1 2 1 2 1 |
f
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2b + 3c
-b 2c find vectors u and v such that w = span u,v |
f
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find a basis for the set of vectors in R 3 in x- 3y + 2z = 0
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r
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find a basis for the subspace spanned by
sin t, sin2t, sintcost |
d
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show that if A is invertible, then det A^-1 = 1/det A
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d
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find a set of vectors that spans W or an example to show that W is not a vector space
4a + 3b 0 a+3b+c 3b-2c |
d
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find a set of vectors that spans W or an example to show that W is not a vector space
1 3a-5b 3b+2a |
d
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is W in nulA?
is W in ColA? what's the rank and what's the dim? 10 -8 -2 -2 2 0 2 2 -2 2 1 -1 6 0 0 1 1 0 -2 2 |
d
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show that H + K is a subspace of V
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d
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Show that H is a subspace of H + K
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d
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determine if it is a subspace of R2, if not give a specific reason why the set is not a subspace
V = x y : x >= 0 , y>= 0 |
d
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W = x
y : xy>=0 determine if it is a subspace of R2, if not give a specific reason why the set is not a subspace |
f
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p(t) = at^2
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d
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p(t) = a + t^2
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d
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degree at most 3 p(t)
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d
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