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QUESTION 1 [38 Marks] 1.1 Consider the $2m \times 2m$ matrix $A = \begin{bmatrix} aI_m & bI_m \ cI_m & dI_m \end{bmatrix}$, where $a$, $b$, $c$ and $d$ are nonzero scalars. 1.1.1 Give an expression for the determinant of A. (7) 1.1.2 For what values of $a$, $b$, $c$ and $d$ will A be nonsingular? (5) 1.1.3 Find an expression for $A^{-1}$. (10)

          QUESTION 1 [38 Marks] 1.1 Consider the $2m \times 2m$ matrix $A = \begin{bmatrix} aI_m & bI_m \ cI_m & dI_m \end{bmatrix}$, where $a$, $b$, $c$ and $d$ are nonzero scalars. 1.1.1 Give an expression for the determinant of A. (7) 1.1.2 For what values of $a$, $b$, $c$ and $d$ will A be nonsingular? (5) 1.1.3 Find an expression for $A^{-1}$. (10)

QUESTION 1 [38 Marks] 1.1 Consider the 2m × 2m matrix A =
< b m a t r i x >, where a, b, c and d are nonzero scalars. 1.1.1 Give an expression for the determinant of A. (7) 1.1.2 For what values of a, b, c and d will A be nonsingular? (5) 1.1.3 Find an expression for A^-1. (10)

Added by Kenneth M.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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1.1 Consider the 2m x 2m matrix A = cIdI, where a, b, c, and d are nonzero scalars. 1.1.1 Give an expression for the determinant of A. 1.1.2 For what values of a, b, c, and d will A be nonsingular? 1.1.3 Find an expression for A^-1.