Suppose that c is the line segment from (a, b) to (c,d). (a) Show that [rd |x dy – y dx = ad – bc Briefly describe what this integral represents geometrically. Hint: Think back to linear algebra. What do determinants measure? (b) Suppose that a polygon P has vertices {(₁, Y₁)}_₁ in counter-clockwise order. Use Green's theorem to show that P has area: 1 A = [(x1Y2 −X2Y1) + (X2Y3 − X3Y2) + ... + (Xn-1Yn — XnYn−1) + (XnY1 − X1Yn)]

Q: Suppose you estimate to be 0.6 -0.5 0.3 T= 0.3 -0.25 0.15 1.2 -1.0 0.6 a. Show that the determinant…

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Q: [1 1 5 2 1 21 (1) Let A = 0 2 B C =|1 3 l3 -1. I-2 3 -21 1. Calculate (if it possible): a) AXB. b)…

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Q: Apply Cramer’s Rule, if possible, to find the value(s) of y from the SLE…

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Q: Find the determinant by using the definition (Big Formula) 1 0 1 0] 1 0 0 1 B : 1 1 1 0 0 1 1

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Q: Q#I (a): Let A = Find a non-zero column vector u = such that Au = 3u. %3D Describe all such vectors.…

A: (a) Let A=134-3  The objective is to find u=xy such that Au=3u The Au=3u can be written as, Au-3u=0…

Q: Find the area of ​​a plane R which has the vertices A(0, 0), B(2, 5), C(6, 3), D(4, -5), and E(0,…

A: We will divide the polygon into sub triangle and then find area of each triangle and then add them…

Q: sketch the set S of points in the complex plane satisfying Im(z) < Re(z)

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Q: 1. Let f(x) = 4x5 - 4x³ + 2x² + 3x - 1. Then use Horner's. method to

A: As you post multiple questions according to guidelines I only solve the first problem . Please post…

Q: n Prove the "column j" expansion for the determinant: det A = (-1)¹¹¹ A¡¡ det áj. i=1

A: We have to prove following determinant formula for any matrix A with respect to "column j". det A =…

Q: Evaluate the determinant using cofactor expansion. Show your work in sim- plifying to a polynomial…

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Q: Can cramer's rule be used to solve this %3D 5 or no? IH vesi unith the determinants used to compute…

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Q: Use the determinant to find 4heValues (k for.. Ax X Such that 3 2 1 A= 7 c) S -3

A: To find the eigenvalues of the given matrices using determinant conidition (equation)

Q: Apply Cramer’s Rule, if possible, to find the value(s) of y from the SLE…

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Q: nted as line v=3 with u=0 to 1 line v=u with u=-3 to 3 line v=3 with u=-1 to 1 lone of these.

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Q: Use coordenadas polares para determinar el volumen del sólido dado. Bajo el cono z = √√x² + y² y…

A: To find the volume of the solid below the cone z = √(x² + y²) and above the ring 1 ≤ x² + y² ≤ 25,…

Q: Recall that the Euclidean scalar product in R² is defined by (x1, Y1) · (x2, Y2) := X1T2+ Y1Y2 - (i)…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: [x+y y+z z+x] If A = then compute the determinant of A. y 1 1 1

A: Given matrix is A=x+yy+zz+xzxy111