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Math 218 Test 3 with Questions and Answer
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Math 218 Test 3 with Questions and Answer Mij ANSWER det(Aij) Cij ANSWER (-1)^(i+j) det(Aij) det(AT) ANSWER det(A) det(AB) ANSWER det(A)det(B) row swap (determinant) ANSWER det(B) = -det(A) row scale (determinant) ANSWER det(B) = c*det(A) row addition (determinant) ANSWER det(B...

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  • November 15, 2024
  • 6
  • 2024/2025
  • Exam (elaborations)
  • Questions & answers

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  • math 218 test 3 with questions and answer

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  • Math 218
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Math 218 Test 3 with Questions and Answer
Mij ANSWER det(Aij)



Cij ANSWER (-1)^(i+j) det(Aij)



det(AT) ANSWER det(A)



det(AB) ANSWER det(A)det(B)



row swap (determinant) ANSWER det(B) = -det(A)



row scale (determinant) ANSWER det(B) = c*det(A)



row addition (determinant) ANSWER det(B)=det(A)



cramer's rule for solving Ax=b ANSWER x=1/det(A) * set of matrices replacing column i
with b



idempotent ANSWER A^2 = A



reciprocal formula ANSWER 1/z = zbar/abs(z)^2



<c*v,w> ANSWER cbar*<v,w>



<v,c*w> ANSWER c*<v,w>

, A* ANSWER ATbar



(AB)* ANSWER B*A*



(A*)* ANSWER A



trace(A*) ANSWER (trace(A))bar



rank(A*) ANSWER rank(A)



det(A*) ANSWER (det(A))bar



Adjoint formula ANSWER <Av,w>=<v,A*w>



eigenvalues of A* ANSWER conjugates of eigenvalues of A



monic ANSWER a polynomial with a leading coefficient of 1



if r is a root of f(t) ANSWER so is rbar



quadratic c0 ANSWER r1*r2



quadratic c1 ANSWER -(r1+r2)



c(n-1) ANSWER -(r1+r2+...+rk)

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