Question

Find the coordinate vector [Bold x ]Subscript Upper B of x relative to the given basis BequalsStartSet Bold b 1 comma Bold b 2 comma Bold b 3 EndSet

Answer 1

The answer to this question can be defined as follows:

Explanation:

In the question equation is missing so, the equation and its solution can be defined as follows:

`B={b_1,b_2}\\\\b_1= \left[\begin{array}{c}5&5\end{array}\right] \ \ \ \ \b_2= \left[\begin{array}{c}2&-5\end{array}\right] \ \ \ \ \x= \left[\begin{array}{c}-7&-35\end{array}\right]`

`\left[\begin{array}{c}a&c\end{array}\right] =?`

`\to \left[\begin{array}{c}-7&-35\end{array}\right]= a\left[\begin{array}{c}5&5\end{array}\right]+c \left[\begin{array}{c}2&-5\end{array}\right] \\`

`\to \left[\begin{array}{c}-7&-35\end{array}\right]= \left[\begin{array}{c}5a+2c&5a-5c\end{array}\right]\\\\\to 5a+2c=-7....(1)\\\\\to 5a-5c=-35....(2)\\\\`

subtract equation 1 from equation 2:

`\to 7c=28\\\\\to c=(28)/(7)\\\\\to c= 4\\\\`

put the value of c in equation 1

`\to 5a+2(4)=-7\\\to 5a+8=-7\\\to 5a=-7-8\\\to 5a=-15\\\to a= -3`

coordinate value is [-3,4].