Problem 3 Calculate the 4th order Taylor polynomial of the following function at the point (0,0). f(x, y) = e(x² + y²)
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- Problem 1: Consider the following two square matrices A=[2345], B=[5−32−6] Find A + B and A-2B Find the products AB and BA. Is AB = BA, why or why not? Is A a singular matrix, why or why not? Problem 2: Find the determinant of A, that is |A|, if A=⎡⎢⎣230−15−3042⎤⎥⎦Problem 3: Find the determinant of AT, that is |AT|, using Matrix A defined in problem 2 aboveProblem 4: Find the inverse of a 2 X 2 matrix B defined in problem 1 aboveQuestion 2 The value of the determinant of the matrix 5A, where A is a square matrix of order 2 and det(A)=3 is 70. - True - False. (a) What is the 2 × 2 matrix P that projects v = x y onto the x axis, i.e. takes x y to x 0 ? Is P invertible? (b) Let ` be the line from problem 2(b). Find the 2 × 2 matrix that projects v = x y onto ` by using a composition method similar to problem 2(b). Please solve both part , thank you
- Suppose A is a 5 by 5 matrix. Its entries in row 1 multiply determinants (cofactors) in rows 2-5 to give the determinant. Can you guess a "Jacobi formula" for det A using 2 by 2 determinants from rows 1-2 times 3 by 3 determinants from rows 3-5? Test your formula on the -1, 2, -1 tridiagonal matrix that has determinant= 6.Question 1 The determinant of a matrix A and its transpose AT differs by negative sign only. - True - FalseIf the determinant of a 4×4 matrix A is det(A)=2, and the matrix D is obtained from A by adding 5 times the third row to the second, thendet(?)=
- 2. If the determinant of a 5×5 matrix A is det(A)=6, and the matrix C is obtained from A by swapping the second and third rows, then what is det(C)? 3. If the determinant of a 4×4 matrix A is det(A)=8, and the matrix D is obtained from A by adding 2 times the fourth row to the first, then what is det(D)?In Problems 7–14, find the value of each determinant.If the determinant of a 3×3 matrix A is det(A)=2, and the matrix B is obtained from A by multiplying the first column by 3, thendet(B)=