For each of the following say whether the matrix A is invert

For each of the following say whether the matrix A is invertible or not. You must give an explanation in each case, you can refer to theorems and results from class. A = matrix. A is an n times n matrix such that the rows of A span R^ n. A is an n times n matrix that is row equivalent to a matrix B and for every b element of R^ n there exists an x element of R^ n such that Bx = b.

Solution

ans(a):

FALSE because first and 4th row are exactly same so determinant will be 0 hence inverse won\'t exist.

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ans(b):

TRUE because rows of A span R^n means they are linearly independent and hence determinant will not be zero so inverse exists.

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ans(c):

TRUE since Bx=b has solution and A and B are equivalent matrices