ISYEl 6669l Midterml Examl Latestl 2025l

ISYEl 6669l Midterml Examl (Latestl 2025/l 2026l Update)l Guide|l Q/Al |l Gradel A|l 100%l Correctl (Verifiedl Answers)

Q:l 2x2l Determinant

Answer:

a11a22l -l a12a21

Q:l Fulll Rank

Answer:

rank(A)l =l min{m,l n}

Ifl ml >l n,l thenl thel systeml hasl nol solution.Ifl ml =l n,l thenl thel systeml hasl al uniquel solutionl xl =l A^−1b.Ifl ml

Q:l Gradientl ofl Vector

Answer:

Partiall derivativel ofl eachl variable.

Q:l Hessianl Matrix

• / 2

Answer:

twicel differentiablel functionl fl atl al pointl x0l isl anl nxl n matrixl ofl second-orderl partiall derivatives

Q:l First-Orderl Taylor'sl Approximation

Answer:

f(x,y)+fx(a,x)(x-a)+fy(a,b)(y-b)

Q:l Closedl Set

Answer:

Al setl isl closedl ifl itl includesl itsl boundaryl points.

Intersectionl ofl closedl setsl isl closed.

Q:l Boundedl Set

Answer:

Al setl isl boundedl ifl itl canl bel enclosedl inl al largel enoughl (hyper)-spherel orl al box

Q:l Compactl Set

Answer:

closedl andl boundedl set

• / 2