MidIISamplev3

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Unformatted text preview: TRUE or FALSE . Along with your answer, provide a counterexample, an informal proof or an explanation. (a) The determinant is a linear function M n × n ( F ) → F . Name and SID: 2 (b) Every n × n matrix may be written as a product of elementary matrices. Name and SID: 3 (c) If Ax = 0 has exactly one solution, then Ax = b has exactly one solution. Name and SID: 4 2. Use row operations to ﬁnd the inverse of the matrix -2 1 4-3 1 1 1-1 . Name and SID: 5 3. Let A be an m × n matrix of rank m and let B be an n × p matrix with rank n . Determine the rank of the matrix AB . Name and SID: 6 4. If a matrix B is similar to matrix C , show that B 2 is similar to C 2 ....
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