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- If the rows of an m cross times n matrix A are linearly independent and Ax=b is consistent then it has unique solution. Select one: True FalseSuppose 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?Let A be 3x5 matrix. Then AX=b has always infinitly many solutions.
- A cellphone provider classifies its customers as low users (less than 400 minutes per month) or high users (400 or more minutes per month). Studies have shown that 80% of people who were low users one month will be low users the next month, and that 70% of the people who were high users one month will high users next month. a. Set up a 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions b. Suppose that during the month of January, 50% of the customers are low users. What percent of customers will be low users in February? In March?Place the smallest number of zeros in a 4 by 4 matrix that will guarantee det A = 0. Place as many zeros as possible while still allowing det A# 0.A cellphone provider classifies its customers as low users (less than 400 minutes per month) or high users (400 or more minutes per month). Studies have shown that 40% of people who were low users one month will be low users the next month and that 30% of the people who were high users one month will high users next month. a. Set up a 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions b. After many months, how many % of the customers are high users
- Calculate X1, X2, X3, and X4 using Gaussian elimination methodOne can use the equations of the Markowitz model to derive the CAPM equation. At thispoint, one would be wrong to conclude that this is the CAPM model. What additional argumentis necessary to make the transition from one model to the other?a. All other options are necessary.b. There is a single investor who holds the mean-variance efficient portfolio.c. There is at least one investor who holds the market portfolio.d. Investors know the returns and standard deviations of all securities in the economy.Can the null space of a 3 × 6 matrix have dimension 2? Explain.