Evaluate the following, round your answers in 2 decimal digits. 5 5 3\ 1.A= 2 -1 3. Solve A-¹ using co-factor 0 2 -1 method. 2. Referring from item 1, calculate AA-¹ = I. In general, therefore, what is I? Is it a matrix? What are its elements?
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- Suppose A is invertible and you exchange its first two rows to reach B. Is the new matrix B invertible? How would you find B-1 from A-1?I don’t understand here how they got the associated matrix like the part with f(1,0,0,0) and so on are they substituting in the coordinates or in alpha or both ?How would I got about solving this question / prove that A is a nxm matrix?
- To divide the LHS by a matrix on the RHS, what steps do you follow?How did we get from the matrix above to the matrix in the bottom in part c?"It is known that 0 is an eigenvalue with algebraic multiplicity 2 of the matrix A given below" I would be so glad if you solve this problem as quick as possible! Thank you! Sorry for poor quality of the image, but anyways the question and options are clear I think
- I'm having a hard time understanding how they're getting these vectors from the matrix. I follow up to plugging in the eigenvalues and solving the variables, then I get lost for like the first one beta = alpha = 0. When I solve and plug in beta = 2*alpha = 2 * (2*beta) -> beta = 4beta, so is it zero because thats the only number that makes this equality? So like it's not so much algebra after solving as looking at the equality and making sense of it?Solve the following systems of equations using the matrix method. Find eigenvalues and eigenvectorsby hand (but you can use technology to check your answers) (NOTE: Please only solve part (b).)Write down what it means for a n x k matrix to be singular.