Question

Let T(x) = Ax for the given matrix A, and find T(u1) and T(u2) for the given u1 and u2. A = 4 2 −5 6 , u1 = −4 −3 , u2 = 2 −5 T(u1) = -22 2 .

Answer 1

T(u1) =
`\left[\begin{array}{c}-22\\2\end{array}\right]`, T(u2) =
`\left[\begin{array}{ccc}-2\\-40\end{array}\right]`

Step-by-step explanation: Matrix A =
`\left[\begin{array}{ccc}4&2\\-5&6\end{array}\right]`, u1 =
`\left[\begin{array}{ccc}-4\\-3\end{array}\right]`, u2 =
`\left[\begin{array}{ccc}2\\-5\end{array}\right]`

If T(x) = Ax and it wants to find T(u1), it means

T(u1) =
`\left[\begin{array}{ccc}4&2\\-5&6\end{array}\right]` ·
`\left[\begin{array}{ccc}-4\\-3\end{array}\right]` =
`\left[\begin{array}{ccc}4.(-4)+2.(-3)\\(-5).(-4)+6.(-3)\end{array}\right]` =
`\left[\begin{array}{c}-22\\2\end{array}\right]`

To find T(u2):

T(u2) =
`\left[\begin{array}{ccc}4&2\\-5&6\end{array}\right]` ·
`\left[\begin{array}{ccc}2\\-5\end{array}\right]` =
`\left[\begin{array}{ccc}4.2+2.(-5)\\(-5).2+6(-5)\end{array}\right]` =
`\left[\begin{array}{ccc}-2\\-40\end{array}\right]`