Exam 7: Matrices

If A, B and C are matrices with orders 3×3, 2×3 and 4×2 respectively, how many of the following matrix calculations are possible? 4B, A + B, 3B^T + C, AB, B^TA, (CB)^T, CBA

Find the value of a if the following matrix is singular $\left[ \begin{array} { l l } - 4 & 2 \\- 6 & a\end{array} \right]$

Find the cofactor, A23, of the matrix $A = \left[ \begin{array} { r r r } 5 & - 2 & 7 \\6 & 1 & - 9 \\4 & - 3 & 8\end{array} \right]$

Find the determinant of the matrix $\left[ \begin{array} { r r r } 5 & - 2 & 3 \\4 & - 1 & - 5 \\6 & 7 & 9\end{array} \right]$

Which one of the following matrices has an inverse which is not listed? $A = \left[ \begin{array} { l l } 1 & 1 \\ 1 & 0 \end{array} \right] , B = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right] , C = \left[ \begin{array} { l l } 0 & 1 \\ 1 & - 1 \end{array} \right] , D = \left[ \begin{array} { r r } 1 & - 1 \\ 1 & 0 \end{array} \right] , E = \left[ \begin{array} { l l } - 1 & 0 \\ 0 & 1 \end{array} \right]$

One unit of I1 uses 0.2 units of I1 and 0.6 units of I2. One unit of I2 uses 0.4 units of I1 and 0.2 units of I2. Find the associated Leontief inverse.

For the commodity market C = aY + b and I = cr + d For the money market MS = MS* and MD = k1Y + k2r + k3 If both markets are in equilibrium, find the matrix A such that Ax = b where $\mathbf { x } = \left[ \begin{array} { l } \boldsymbol { r } \\\bar { Y }\end{array} \right] \text { and } \mathbf { b } = \left[ \begin{array} { c } M _ { S } { } ^ { * } - k _ { 3 } \\b + d\end{array} \right]$

$\left[\begin{array}{lrr}3 & -2 & -7 \\-4 & 5 & 1 \\3 & 0 & 6\end{array}\right]$ -Matrices, A, B and C are given by $A=\left[\begin{array}{lrr}3 & -2 & 4 \\6 & 1 & 0 \\-5 & 9 & 5\end{array}\right]$ $B=\left[\begin{array}{llr}1 & 5 & 0 \\-8 & 4 & 7 \\2 & 3 & -9\end{array}\right]$ $C=\left[\begin{array}{lrr}3 & -2 & -7 \\-4 & 5 & 1 \\3 & 0 & 6\end{array}\right]$ If D = A(2B + 3C)find d₂₃.