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- Determine the eigenvalues of the matrix you have determined. 3 3 -3 3 - Find at least one corresponding eigenvector from the eigenvalue that• Use the definition of Laplace transform to find L{f (t)} for the given f (t). a) f(t) = cos2(t – n) %D b) f(t) = 2 sin 3t cos 3t 2 c) f(t) = sinh t 3Answer the following: 1. Write an example of a matrix multiplication that is undefined. 2. If the expression A x B is defined, and if A is a 3 x 5 matrix, then what could be the dimensions of B? 3. Define Matrix multiplication in your own words. 4.Matrix C has dimensions 2 x 3, Matrix D has dimensions 2 x 3, and matrix F has dimensions 3 x 2. Find the dimensions of the following products: a. CD b. DF c. FC 11 Explain all your answer for each question use Reply"
- Suppose the determinant of a 3 x 3 matrix A is equal to 5. What is the determinant of -2A?4. Two matrices A and B are multiplied to get AB if: A. both are rectangular of B C. number of columns of A is equal to number of rows B. both have the same order D. number of rows of A is equal to number of columns of B4.A.1. Is there a real number whose square is -1? a. Is there a real number x such that ? O x = -1 O x*2 = -1 4.A.1. Is there a real number whose square is -1? b. Does there exist such that x^2= -1? a number a real number 4.A.2. Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3 when it is divided by 6? a. Is there an integer n such that n has ? a remainder of 5 when it is divided by 2 and a remainder of 3 when it is divided by 6 a remainder of 2 when it is divided by 5 and a remainder of 3 when it is divided by 6
- = A, and skew-symmetric if AT = −A. 1. A square matrix A is said to be symmetric if AT Give an example of (a) a symmetric matrix of order 3 (b) a skew-symmetric matrix of order 3Format: . If your answer below is a vector, input it as a column vector using the vector/matrix palette tool. . Use to explicitly indicate multiplication between variables and other variables, between variables and brackets, or between sets of brackets (e.g. x*y rather than xy; 2*(x+y) rather the . Put arguments of functions in brackets (e.g. sin(x) rather than sin x). Consider the vector field Calculate the divergence of a. V.a= Calculate the curl of a. Vxa= Q A 2 € W S £ 3 # E D $ 4 R G Search or type URL F % 5 a = (-90.2² y+5-y)i + (-47-z-y-60-y-z)j + ( T MacBook Pro 6 G Y & 7 H U 8 ✪ JU ( 1 9 A K ) .O 3 0 0 +(-8.². z+18-2) k. P J +