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MATH311Midterm1Practice

# MATH311Midterm1Practice - Math 311.503/505 Practice for...

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Math 311.503/505 - Practice for Midterm 1 1. Answer TRUE or FALSE. – i) The set of all n × n symmetric matrices is a vector space. – ii) The set of all positive continous functions on [0 , 1] is a vector space. – iii) The set { 1 ,x,x 2 } is a basis for the vector space of all polynomials of degree 2. – iv) Product of elementary matrices is also an elementary matrix. – v) If the n × n matrix A is row equivalent with the identity then A is non- singular. – vi) Let A be a m × n matrix. Then N ( A ) = N ( A T ). – viii) Let A be a n × n matrix. Then det( A ) = det( A T ). 2. Use Gaussian elimination to solve the following system: x 1 - x 2 + 3 x 3 + 2 x 4 = 1 - x 1 + x 2 - 2 x 3 + x 4 = - 2 2 x 1 - 2 x 2 + 7 x 3 + 7 x 4 = 1 . 3. Find the values of x such that the matrix x 1 0 1 1 x - 1 0 0 - 1 x 1 1 0 1 x 4. Let A be the 4 × 5 matrix 1 0 - 1 4 1 - 1 0 2 1 0 0 1 3 1 1 - 1 1 1 0 15 Find a basis for the null space of

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MATH311Midterm1Practice - Math 311.503/505 Practice for...

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