For the equation ax^2 + bxy + cy^2 = 0, let A = [a b/2 b/2 c] (A is a 2x2 matrix) Show that if det(A) = 0, then the graph of ax^2 + bxy + cy^2 = 0 is a line. Show that if det(A) != 0, then the graph of ax^2 + bxy + cy^2 = 0 is two intersecting lines.

Q: rewrite ax^2+by^2+cz^2+dxy+exz+fyz+gx+hy+iz+j=0 in  standard form by matrix

A: The objective of the question is to rewrite the given quadratic equation in three variables in…

Q: If any three square matrices have the same size as A ,B,C AB=I and CA=I prove that A=C=A^-1

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Q: Also, how is the second to last 4x4 matrix on the last page is found?

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Q: For matrix A and a scalar k, (kA)T is equal to: k(A^T) k(A) (k^2) x (A) (k^2) x (A^T)

A: We will solve the matrix operation.

Q: 2. A = 77₁b = 3 25 -1 3

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Q: A matrix is called skew-symmetric if A^T = −A. If A is a n × n matrix, then show the following: i.…

A: Solution:Given: is any matrixwe have to show that(i). The matrix is symmetric(ii). The matrix is…

Q: 2. Describe the geometry of the linear transformation represented by each matrix. Explain. 3 0 a. ^=…

A: Follow the steps.

Q: 3) Without graphing, determine the number of solutions for (x + 2y3z = 9 [y-3x = 6 (3y - 9x = 18

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Q: Use a matrix to solve x - y + 5z = 194x + z = 3x + 3y + z = -9A) (3, 0, -4) B) (3, -4, 0) C) (0, -4,…

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Q: True or False? Justify your answer. a) Let A, B, and C be two square matrices of the same dimension…

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Q: Calculate A^-1 and use it to solve the matrix equations 1 12 5 12 ²2). 5 = ( − 3), 5₂ = ( ¹3 ). -5 A…

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Q: If matrix A, B and C are invertible matrix of same order then (ABC)^(-1) = * C^-1) x B^(-1) x A^(-1)…

A: Given that A,B and C are invertible matrices of the same order.

Q: Let A, B, C be invertible n x n matrices. SOLVE for A in: A^-1B^-1 = C^-1

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Q: Solve the matrix equation AX = B, where -1 하 A: 1 and B 1 1 [6] 0 1 =

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Q: Find a real matrix A such that A ^6 = (09, -90)

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Q: solve for x and y in the matrix A= [ x -4 3 y] if A^2 = [52 -36  27  -11] x = y =

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Q: Solve for x and y in the matrix A=[x 3 2 y] if A^2 = [ 31 12 8 87] x = y =

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Q: The following matrix product is used in discussing two thin lenses in air: (1 -1/f2 M where fi and…

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Q: Use the Gaussian algorithm to determine the inverse matrix A^-1.   A = 1  2  1 0  1   3 2  4   1

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Q: Suppose A, B, and X are n x n matricies with A, X, and A - AX invertible and suppose (A - AX)^-1 =…

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Q: Create a 3x3 matrix A with a determinant of 10. Then, compute the matrix of cofactors of A and the…

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Q: Show that if A is a square matrix that satisfies the equation 2 A²-A-I-O, then its inverse is A-¹ =…

A: A square matrix M is said to be invertible if det(M)≠0 . If M is invertible,  then MM-1=I=M-1M ,…

Q: for part b), how can you multiply the E1^-1 and A as they are not the same size matrix? is that…

A: Given that encryption matrix A is of size 2 x 4.   Now, from rule of multiplication of matrices in…

Q: Let A = [0 1 0 0 ], A^(-1) is equal to: * Does not exist Identity matrix Null matrix

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Q: ^ = [1 ] A If A is diagonalizable, find an invertible 2 x 2 matrix P and a 2 x 2 diagonal matrix D…

A: Given that the matrix A=0-440. If the given matrix is diagonalizable , find an invertible matrix and…

Q: for Find property 8. Give matrix A and constants c and d so that Cc+d) @ A# (COA) + (LOA) a…

A: To give a counterexample to property c+d⊗A≠c⊗A⊕d⊗A. Here A is a matrix and c, d are scalars. The…