You visited us 1 times! Enjoying our articles? Unlock Full Access!

Solving Simultaneous Linear Equation Using Cramer's Rule

Let c1,.........

Question

Let $c_{1}, . . . . . . . . ., c_{n}$ be scalars, not all zero, such that $\sum_{i = 1}^{n} c_{i} a_{i} = 0$ where $a_{i}$ are column vectors in $R^{n}$ Consider the set of linear equations Ax=b.
where A= $[a_{1}, . . . . . ., a_{n}]$ and $b = \sum_{i = 1}^{n} a_{i}$ .The set of equations has

a unique solution at

x = j_{n}

where

j_{n}

n denotes a n-dimensional vector of all 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

no solution

No worries! We‘ve got your back. Try BYJU‘S free classes today!

infinitely many solutions

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

finitely many solutions

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C infinitely many solutions
Since the scalars are not all zero so liner convolution exist.
Hence, the column vectors $a_{1}$ for I=1,2,.....n is linearly dependent

Suggest Corrections

Similar questions

a_{1} = 0

a_{1}

a_{2}

a_{3}

a_{n}

| a_{i} | = | a_{i - 1} + 1 |

a_{1}

a_{2}

a_{3}

a_{n}

\times

A^{2} = I

c_{1}, c_{2}, \dots, c_{n}

a = (a_{1}, a_{2}, \dots, a_{n})

(1, 2, \dots, n)

S (a) = n \sum i = 1 c_{i} a_{i} .

a \neq b

{1, 2, \dots, n}

a_{1}, a_{2}, . . ., a_{100}

a_{1} + a_{2} + . . . + a_{100} = 0

a_{1}, a_{2}, . . . . . . . a_{n}

(c_{1}, c_{2} - - - c_{n} s u c h t h a t c_{1} ¯ a + c_{2}_{2} + . . . c_{n}_{n} = ¯ 0

Join BYJU'S Learning Program