Daily LinAlg T/F Questions @LinAlgDaily

Posting daily true/false questions relating to undergraduate linear algebra. Please comment proofs/counterexamples. Link below for question and solution bank. docs.google.com/spreadsheets/d… Joined December 2022

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Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

Happy Pi Day.

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

T/F: it is possible that A is an invertible matrix and A is the standard matrix for a non-injective function

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

Hard mode: T/F: suppose A and B are matrices such that AB is defined. Any vector in col(AB) is also in col(A)?

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

T/F: a vector may be in colA and also in Null A?

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

T/F: if subspace V is defined V=span{v1, …, vn} then {v1, …, vn} is a basis for V?

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

T/F: any basis for R^n must have exactly n vectors.

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

T/F: if Ax = b and b is not the zero vector then x is certainly not in the null space of A.

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

T/F: if A is mxn and m > n then A^T may not have independent columns

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

T/F: BAx must be in col(A)? Must be in col(B)?

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

T/F: any matrix whose columns form a basis for R^n has pivots every row and every columns.

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

T/F: Let A be mxn. Then Ax is in Col(A) for every x in R^n.

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

If A is size mxn, and b is in Col(A) for every b in R^m, the the transformation T: R^n |-> R^m defined by T(x)=Ax is onto (surjective).

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

T/F: let A be a 3x4 matrix. Then the transformation whose standard matrix is A cannot be onto.

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

Gonna go on a solutions release spam on some recent tweets

Daily LinAlg T/F Questions @LinAlgDaily

3 years ago

T/F: If P is a permutation matrix then P^n=I for some n

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