Recent questions tagged system-of-equations

The $a, b, c$ and $d$ satisfy the equations$$\begin{matrix} a & + & 7b & + & 3c & + & 5d & = &16 \\ 8a & + & 4b & + & 6c & + & 2d & = &-16 \\ 2a & + & 6b & + & 4c & + & 8...

Consider following system of equations:$\begin{bmatrix} 1 &2 &3 &4 \\ 5&6 &7 &8 \\ a&9 &b &10 \\ 6&8 &10 & 13 \end{bmatrix}$$\begin{bmatrix} x1\\ x2\\ x3\\ x4 \end{bmatri...

If $a,b,c$ and $d$ satisfy the equations$a+7b+3c+5d =16$$8a+4b+6c+2d = -16$$2a+6b+4c+8d = 16$$5a+3b+7c+d= -16$Then $(a+d)(b+c)$ equals$-4$$0$$16$$-16$

For what values of $\lambda$ the system of equations will have $2$ linear independent solutions -$x + y + z = 0$$(\lambda + 1) y + (\lambda + 1) z = 0$($\lambda^{2}- 1) z...

How to solve?________________Number of non-negative integer solutions such thatx+y+z=17where x>1,y>2,z>3 is

how to solve such questions?

Let A be an nxn real matrix such that A^2=I and y be an n-dimensional vector. Then the linear system of equations AX=Y hasA) No solutionB) Unique SolutionC) More than one...

Consider a system of equations (λ – a)x + 2y +3z = 0, x +2(λ – b) y + 3z = 0, x + 2y + 3(λ – c) z = 0, which has a non-trivial solution. Product of all values of λ for a...

Consider the following system system of equationsx1-2x3=0x1-x2=02x1-2x2=0 No solution Infinite number of solutions Three solutionunique solution

The system of equations $x + y + z = 6, 2x + y + z = 7, x + 2 y + z = 8$ hasA unique solutionNo solutionAn infinite number of solutionsNone of these

Let $Ax = b$ be a system of linear equations where $A$ is a $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is a $n \times 1$ ...

$A$ is $3 \times 4$-matrix of rank $3$. Then the system of equations,$Ax = b$has exactly one solution.