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This is the Quiz of Linear Algebra which includes Satisfies the Conditions, Information, Explicit Conditions, Guarantee, Conditions, Basis, Linear Combination, Basis Vectors, Column Vector, Bottom Entry etc. Key important points are: Reason, Determinant, Matrix, Swapping Rows, Derivative, Integral, Elementary Row Operations, Main Diagonal Entries, Multiplied, Triangular Matrix
Typology: Exercises
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Math 205 A B Quiz 06 gold page 1 11/02/2012 Name
a b c r s t
; suppose det(B)=
Find the determinant of each of the following matrices, and under each matrix write the reason/rule/fact about determinants of matrices you used to find the det. (eg, “swapping rows changes the sign of the det” or “the determinant of the derivative of a matrix is the matrix of its integral” (this second fact is nonsense)
2a) M =
1 a r 2 b s 4 c t
(^) 2b) N =
a b c r + 2 s + 4 t + 8
2c) Q =
a b c r s t
(^) 2d) R =
a b c 1 2 4
2e) S = 4B
3B) Is A invertible? Explain how you know.