2 For each of the augmented matrices below determine if the

2. For each of the augmented matrices below, determine if the associated system of linear equations is inconsistent, has a unique solution, or has infinitely many solutions. 3. Is the following 10 x 10 matrix A invertible? Why or why not? (The (i, j)-entry of A is 0 if i > j, and is j if i

Solution

Ans(2):

look at last row of A1. we get equation 0=0 which is true.

Hence the system has infinitely many solutions.

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look at last row of A2. we get equation 0=2 which is FALSE.

Hence system is Inconsistent.

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In A3, we have 3x4 matrix means 3 equations and 4 variables.

Since number of variables is more than number of equations so yhe system has infinitely many solutions

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Ans(3):

we see given matrix A is an upper triangular matrix. We know determinant of upper triangular matrix is given by just multiplication of its diagonal entries.

Hence determinant(A)=1*2*3*4*5*6*7*8*9*10=3628800

since determinant is non-zero, Hence given matrix is Invertible.