Let A = beginpmatrix1&0&0 2&1&0 3&2&1 endpmatrix If u1 and u2 are column matrices such that Au1 = beginpmatrix1 0 0 endpmatrix and Au2 = beginpmatrix0 1 0 endpmatrix, then u1 + u2 is equal to :

Question

Let A = beginpmatrix1&0&0 2&1&0 3&2&1 endpmatrix If u1 and u2 are column matrices such that Au1 = beginpmatrix1 0 0 endpmatrix and Au2 = beginpmatrix0 1 0 endpmatrix, then u1 + u2 is equal to : (A)  beginpmatrix-1 1 0 endpmatrix (B)  beginpmatrix- 1 1 -1 endpmatrix (C)  beginpmatrix -1 -1 0 endpmatrix (D)  beginpmatrix1 -1 -1 endpmatrix

Tardigrade Admin · Accepted Answer

A(u1+u2) = beginpmatrix1 1 0 endpmatrix |A| = 1 A-1 = (1/|A|)adj A u1 + u2 = A-1 [1 1 0] A-1 = [1&0&0 -2&1&0 1&-2&1] = [1 -1 -1]

Q. Let $A = ⎝ ⎛ 123012001 ⎠ ⎞$ If $u_{1}$ and $u_{2}$ are column matrices such that $A u_{1} = ⎝ ⎛ 100 ⎠ ⎞$ and $A u_{2} = ⎝ ⎛ 010 ⎠ ⎞,$ then $u_{1} + u_{2}$ is equal to :

$⎝ ⎛ - 1 10 ⎠ ⎞$

$⎝ ⎛ - 1 1 - 1 ⎠ ⎞$

$⎝ ⎛ - 1 - 1 0 ⎠ ⎞$

$⎝ ⎛ 1 - 1 - 1 ⎠ ⎞$

$A (u_{1} + u_{2}) = ⎝ ⎛ 110 ⎠ ⎞ ∣ A ∣ = 1$
$A^{- 1} = \frac{1}{∣ A ∣} a d j A$
$u_{1} + u_{2} = A^{- 1} ⎣ ⎡ 110 ⎦ ⎤ A^{- 1} = ⎣ ⎡ 1 - 2 1 01 - 2 001 ⎦ ⎤ = ⎣ ⎡ 1 - 1 - 1 ⎦ ⎤$

Q. Let A=⎝⎛​123​012​001​⎠⎞​ If u1​ and u2​ are column matrices such that Au1​=⎝⎛​100​⎠⎞​ and Au2​=⎝⎛​010​⎠⎞​, then u1​+u2​ is equal to :

⎝⎛​−110​⎠⎞​

⎝⎛​−11−1​⎠⎞​

⎝⎛​−1−10​⎠⎞​

⎝⎛​1−1−1​⎠⎞​