If A= beginpmatrixα-1 0 0 endpmatrix, B= beginpmatrixα+1 0 0 endpmatrix be two matrices, then ABT is a non-zero matrix for |α| not equal to

Question

If A= beginpmatrixα-1 0 0 endpmatrix, B= beginpmatrixα+1 0 0 endpmatrix be two matrices, then ABT is a non-zero matrix for |α| not equal to (A) 2 (B) 0 (C) 1 (D) 3

Tardigrade Admin · Accepted Answer

Let A= beginpmatrixα-1 0 0 endpmatrix, B= beginpmatrixα+1 0 0 endpmatrix be two matrices. ABT= beginpmatrixα -1 0 0 endpmatrix(α+1 0 0) = beginpmatrixα2-1&0&0 0&0&0 0&0&0 endpmatrix Thus, ABT is non-zero matrix for |α| ≠ 1

Q. If $A = ⎝ ⎛ α - 1 00 ⎠ ⎞, B = ⎝ ⎛ α + 1 00 ⎠ ⎞$ be two matrices, then $A B^{T}$ is a non-zero matrix for $∣ α ∣$ not equal to

$2$

$0$

$1$

$3$

Let $A = ⎝ ⎛ α - 1 00 ⎠ ⎞, B = ⎝ ⎛ α + 1 00 ⎠ ⎞$
be two matrices.
$A B^{T} = ⎝ ⎛ α - 1 00 ⎠ ⎞ (α + 100)$
$= ⎝ ⎛ α^{2} - 1 00 000000 ⎠ ⎞$
Thus, $A B^{T}$ is non-zero matrix for $∣ α ∣ \neq = 1$

Q. If A=⎝⎛​α−100​⎠⎞​,B=⎝⎛​α+100​⎠⎞​ be two matrices, then ABT is a non-zero matrix for ∣α∣ not equal to

2

0

1

3

Let A=⎝⎛​α−100​⎠⎞​,B=⎝⎛​α+100​⎠⎞​ be two matrices. ABT=⎝⎛​α−100​⎠⎞​(α+100) =⎝⎛​α2−100​000​000​⎠⎞​ Thus, ABT is non-zero matrix for ∣α∣=1

Q. If $A = ⎝ ⎛ α - 1 00 ⎠ ⎞, B = ⎝ ⎛ α + 1 00 ⎠ ⎞$ be two matrices, then $A B^{T}$ is a non-zero matrix for $∣ α ∣$ not equal to

$2$

$0$

$1$

$3$

Let $A = ⎝ ⎛ α - 1 00 ⎠ ⎞, B = ⎝ ⎛ α + 1 00 ⎠ ⎞$
be two matrices.
$A B^{T} = ⎝ ⎛ α - 1 00 ⎠ ⎞ (α + 100)$
$= ⎝ ⎛ α^{2} - 1 00 000000 ⎠ ⎞$
Thus, $A B^{T}$ is non-zero matrix for $∣ α ∣ \neq = 1$