a student wrote the matrix below to represent the solution to a system of equations.\n\\\\begin{bmatrix}1&0&5…

a student wrote the matrix below to represent the solution to a system of equations.\n\\\\begin{bmatrix}1&0&5&-2\\\\0&0&3&0\\\\0&0&0&-1\\end{bmatrix}\\\nwhich of the following describes the solution?\nno solution\nan infinite number of solutions\n(-2, 0, -1)\n(5, -2, -1)

a student wrote the matrix below to represent the solution to a system of equations.\n\\\\begin{bmatrix}1&0&5&-2\\\\0&0&3&0\\\\0&0&0&-1\\end{bmatrix}\\\nwhich of the following describes the solution?\nno solution\nan infinite number of solutions\n(-2, 0, -1)\n(5, -2, -1)

Answer

Explanation:

Step1: Convert the augmented matrix to equations.

The augmented matrix represents the following system of linear equations, assuming variables $x$, $y$, and $z$: $$ \begin{cases} 1x + 0y + 5z = -2 \ 0x + 0y + 3z = 0 \ 0x + 0y + 0z = -1 \end{cases} $$ This simplifies to: $$ \begin{cases} x + 5z = -2 \ 3z = 0 \ 0 = -1 \end{cases} $$

Step2: Analyze the last equation.

The last equation, $0 = -1$, is a contradiction. It is mathematically impossible.

Step3: Determine the nature of the solution.

Since the system leads to a contradiction, there are no values of $x$, $y$, and $z$ that can satisfy all equations simultaneously. Therefore, the system has no solution.

Answer:

no solution