Practicing Success
If A = \(\begin{bmatrix}4 & 10\\2 & 1 \end{bmatrix}\), then what is the value of |\(3 { A }^{ T } \)|? |
48 144 -48 -144 |
-144 |
If Matrix A has size a × a and k is a constant, then |kA| = \( { k }^{ a } \) |A| Then, |\(3 { A }^{ T } \)| = \( { 3 }^{ 2 } \) |\( { A }^{ T } \)| = \( { 3 }^{ 2 } \) |A | Because |\( { A }^{ T } \) = |A | |\(3 { A }^{ T } \)| = 9 |A | And |A | = -16 So, |\(3 { A }^{ T } \)| = -144 |