Download M340L Unique number 53280

M340L Unique number 53280
Solution of the practice quizzes #2
1st practice quiz
TRUE
1)A homogeneous equation is always consistent.
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2) The solution set of Ax = b is obtained by translating
the solution set of Ax = 0
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3) If S is a linearly independent set, each vector is a linear
combination of the other vectors in S
4) If x and y are linearly independent , and z is in Span (x,y)
then {x, y, z} is linearly dependent
FALSE
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5) If v1, … , v4 are in R4 and v3 is not a linear combination
of v1, v2, v4, then { v1, v2, v3, v4}is linearly independent.
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6) If A is a 5x4 matrix, the linear transformation x  Ax
cannot map R4 onto R5 (i. e. the range cannot be R5).
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7) If A is an invertible nxn matrix, then the equation Ax = b
is consistent for each b in Rn.
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8) If an nxn matrix A is invertible, then its columns are
linearly independent .
9) If A is an nxn matrix such that the equation Ax = 0 has a
non trivial solution, then A has fewer than n pivot positions.
10) Let A and B be 2 square matrices. If AB is invertible so
is B. (Hint: if Bx=0, then ABx=0)
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2nd practice quiz
TRUE
1) The solution set of Ax = b is the set of all vectors of
the form w = p + vh , where vh is any solution of the
equation Ax = 0, and Ap = b.
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2) If v1, … , v4 are linearly independent vectors in R4,
then { v1, v2, v3} is also linearly independent.
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3) Two vectors are linearly dependent if and only if
they lie on a line through the origin.
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4) If none of the R3 vectors in the set S = { v1, v2, v3}
is a multiple of one of the other vectors, then S is
linearly independent.
5) If A is invertible, the inverse of A-1 is A itself.
6)If (B-C)A = 0, where B and C are mxn matrices and
A is invertible, then B = C.
7) If for an nxn matrix A, the equation Ax = b has a
solution for each b in Rn, then A is invertible.
8) If the columns of an nxn matrix A span Rn, then the
columns of A are linearly independent.
9) Let A and B be square nxn matrices. If AB is invertible,
so is A. (Hint: if AB is onto, is A onto?)
10) If A is invertible and r different from 0, (rA)-1 = rA-1.
FALSE
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