Respuesta :
Answer:
For h= 25, b in the plane spanned by a1 and a2
Step-by-step explanation:
[tex]a1= \left[\begin{array}{c}1\\2\\-1\end{array}\right] \\a2 = \left[\begin{array}{c}-7\\-7\\2\end{array}\right] \\\\b = \left[\begin{array}{c}3\\-22\\h\end{array}\right][/tex]
we have to find value of h for which b in the plane spanned by a1 and a2.
For this the linear systems given by the following augmented matrix must be consistent.
[tex]\left[\begin{array}{cc|c}1&-7&3\\2&-7&-22\\-1&2&h\end{array}\right][/tex]
Reduce the augmented matrix into row echelon form:
[tex]R_{2} - 2R_{1} , R_{3} + R_{1}\\\\\left[\begin{array}{cc|c}1&-7&3\\0&7&-28\\-0&-5&h+3\end{array}\right]\\\\7R_{3}+5R_{2}\\\\\left[\begin{array}{cc|c}1&-7&3\\0&7&-28\\-0&0&7h-175\end{array}\right][/tex]
For system to be consistent:
[tex]7h-175 =0\\7h=175\\h=25[/tex]
