Quiz
linear
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Questions in this quiz (23)
1Let A be an n x n matrix. The system Ax = b is consistent if every column of A has a pivot.
- ATrue
- BFalse
2If u, v, and w are vectors in R^3 and are linearly independent, then they span R^3.
- ATrue
- BFalse
3Let A be an n x n matrix. Then the system Ax = 0 has infinitely many solutions if A is invertible.
- ATrue
- BFalse
4If the system Ax = 0 has a non-trivial solution, then it has infinitely many solutions.
- ATrue
- BFalse
5If A is an n x n matrix and columns of A are linearly independent, then A is an invertible matrix.
- ATrue
- BFalse
6If the second row of the matrix A is a zero row, then the second row of AB is also zero.
- ATrue
- BFalse
7If A and B are invertible matrices, then (AB)^-1 = A^-1B^-1.
- ATrue
- BFalse
8Let A be an invertible matrix. Then the system Ax = b has a solution x = b/A.
- ATrue
- BFalse
9Let A be an invertible matrix. Then detA^-1 = 1/detA.
- ATrue
- BFalse
10If all the diagonal elements of an n x n matrix are zero, then det(A) = 0
- ATrue
- BFalse
11If A is an n x n matrix and Ax = 0 has a nontrivial solution, then the echelon form of A has less than n pivots.
- ATrue
- BFalse
12If {v1, v2, ..., vn} is a linearly independent set in a vector space V, the {v1, v2, ..., vn} is a basis for V.
- ATrue
- BFalse
13If A is a non-invertible n x n matrix, then the columns of A form a basis of R^n.
- ATrue
- BFalse
14The column space of an m x n matrix is R^n
- ATrue
- BFalse
15The number of pivot columns of a matrix equals the dimension of its column space.
- ATrue
- BFalse
16If v1 and v2 are eigenvectors of A, then v1 + v2 is also an eigenvector of A.
- ATrue
- BFalse
17The linear transformation T(x) = [-1 0 ; 0 1]x reflects a figure about the y-axis.
- ATrue
- BFalse
18If the n x n matrix A has n eigenvalues, then A is diagonalizable.
- ATrue
- BFalse
19If T is a linear transformation, the T(au + bv) = aT(u) + bT(v).
- ATrue
- BFalse
20Let T: R^n -> R^m be a linear transformation and {v1, v2, ..., vk} be a linearly independent set in R^n. Then {Tv1, Tv2, ..., Tvk} is a linearly independent set.
- ATrue
- BFalse
21If A and B are similar, then A and B have the same eigenvalues.
- ATrue
- BFalse
22A diagonalizable matrix is always invertible.
- ATrue
- BFalse
23The eigenspace of A corresponding to the eigenvalue lambda is Null(A - lambda * I)
- ATrue
- BFalse
Information
- Description
- Quiz on linear, created by Johnny Catsup on 12/12/2018.
- Author
- Johnny Catsup
- Language
- English
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- Rating
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