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Mathematics, 18.02.2021 08:30 escojo2508

Matrices P and Q are defined by P=\left[\begin{array}{ccc}x&2\\-5&-1\\\end{array}\right] and Q=\left[\begin{array}{ccc}2&-3\\4&y\\\end{array}\right]. Where x, y∈R (a) Given the determinant of P is 2, obtain:

(i) The value of x.

(ii) P^{-1}

(iii) P^{-1}Q'^{-1}, where Q' is the transpose of Q.

(b) The matrix R is defined by R=\left[\begin{array}{ccc}5&-2\\z&-6\\\end{array}\right], where z∈R.

Determine the value of z such that R is singular.

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