We know that.A, B, C are all n times n matrix (so that any product of those matr

Question

We know that.A, B, C are all n times n matrix (so that any product of those matrices is defined Simplify the following expression, by using the properties (clearly indicate nil stops of your simplifications, (ABC)^T - (A(B+C)^T)^T -(BC -B^T)^T A^T. A is a 3 times 3 matrix. We know that each of the systems ax= e_1,Ax = e_1 and Ax =e_3 is consistent. Show that there exists n matrix B with the property that AB = I_3, where I_3 is the identity 3 times 3 matrices Consider the 3 times 3 matrix A = [1 2 3 1 1 4 2 3 6] Finf the inverse A^-1 of A

Explanation / Answer

Since Ax = (e1, e2, e3) is consistent

Determinant A is non zero

Since matrix A is non singular, inverse exists for matrix A

Or there is a matrix B such that

AB = I

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