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MAS Exam 2 T/F

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if A is nxn and detA=2 then detA³=6

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Mar 1, 2020

Cards (30)

Section 1

(30 cards)

if A is nxn and detA=2 then detA³=6

Front

F

Back

the transpose of an elementary matrix is an elementary matrix

Front

T

Back

if A is a 3x3 matrix and the equation Ax=[1] [0] [0] has a unique solution, then A is invertible

Front

T

Back

left-multiplying a matrix B by a diagonal martix A, with nonzero entries on the diagonal, scales the rows of B

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T

Back

if A is a 3x3 matrix, then det5A=5detA

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F

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if AB=BA and if A is invertible, then A⁻¹B=BA⁻¹

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T

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if u and v are in R² and det[u v]=10, then the area of the triangle in the plane with vertices at 0,u, and v is 10

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F

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if A and B are mxn, then both AB^T and A^(T)B are defined

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T

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every square matrix is a product of elementary matrices

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F

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det(-A)=-detA

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F

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if BC=BD then C=D

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F

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an elementary nxn matrix has either n or n+1 nonzero entries

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T

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det^(T)A≥0

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T

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if AB=1 then A is invertible

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F

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if A is a 2x2 matrix with a zero determinant, then one column of A is a multiple of the other

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T

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any system of n linear equation in n variables can be solved by Cramer's rule

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F

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if AB=C and C has 2 columns, then A has 2 columns

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F

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if B is produced by interchanging two rows of A, then detB=detA

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F

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if A and B are square and invertible, then AB is invertible and (AB)⁻¹=A⁻¹B⁻¹

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F

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if B is produced by multiplying row 3 of A by 5, then detB=5(detA)

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T

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an elementary matrix must be square

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T

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if A is a 3x3 matrix with three pivot positions, there exist elementary matrices E₁,...Ep such that Ep...E₁A=I

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T

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if A and B are nxn, then (A+B)(A-B)=A²-B²

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F

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if A and B are nxn matrices, with detA=2 and detB=3 then det(A+B)=5

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F

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if A³

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if AC=0, then either A=0 or C=0

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F

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if A is invertible and r≠0 then (rA)⁻¹=rA⁻¹

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F

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detA^T=-detA

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F

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if B is formed by adding to one row of A a linear combination of the other rows, then detB=detA

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T

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if 2 rows of a 3x3 matrix A are the same, then detA=0

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T

Back