Determine the values of x such that x 2 1 beginbmatrix 2 3 2...

Name: determine the values of x such that x 2 1 beginbmatrix 2 3 2 3 3 1 2 27 1 endbmatrix beginbmatrix x 1 4 endbmatrix 0 x note if there is more than one value separate them by commas 98956
Uploaded: 2024-03-20T10:53:02-08:00
Duration: 6 min 11 s
Channel: Willis James
Description: determine the values of x such that x 2 1 beginbmatrix 2 3 2 3 3 1 2 27 1 endbmatrix beginbmatrix x 1 4 endbmatrix 0 x note if there is more than one value separate them by commas 98956

Determine the value(s) of $x$ such that $[x \ 2 \ 1] \begin{bmatrix} 2 & 3 & -2 \\ 3 & 3 & 1 \\ -2 & -27 & 1 \end{bmatrix} \begin{bmatrix} x \\ -1 \\ -4 \end{bmatrix} = [0]$ $x = $ Note: If there is more than one value separate them by commas.

Transcript

00:01 Hello, welcome to this lesson.

00:02 This lesson will determine the value of values of x like that.

00:06 The matrix x to 1 times the matrix negative 5 to 5, 2, negative 3, negative 3, 5, negative 6, negative 3, times x minus 1, 2 is equal to the zero matrix.

00:26 All right so let's take it one after the other first of all we do this matrix multiplication all right after that we would multiply with the next one okay so what we'll do is that we'll have negative 5 times x all right then we'll have the matrix multiplication goes this way we'll have 2 2 times 2, which is 4.

01:02 Then we have 1 times 5, which is 5.

01:09 Okay.

01:10 Then we have, again, 2 times x.

01:16 That is this.

01:18 Then minus 2 times negative 2 times 3.

01:23 Okay.

01:24 The negative is there, so that makes it 6.

01:27 Then minus, here we'll have 1 times 6.

01:32 Okay.

01:32 Then we'll go to the next one.

01:34 We have 5 times x, which is 5x.

01:40 Then 2 times negative 3, so that makes it negative 6.

01:45 Then 1 times negative 3.

01:49 So that's all times x negative 1, 2 equals to the 0 matrix.

01:58 So let's put that together.

02:00 We'll have negative 5x plus 9.

02:04 Then here we'll have 2x minus 12 and we have 5x minus 9 all right multiplying x1 to equals to the zero matrix okay so here too we have the whole of this multiplying the whole of that so here we'll have x multiply negative 5x plus 9, then negative 1 multiplying 2x minus 12, then we have positive 2 multiplying 5x minus 9, and this is equal to 0.

02:50 0.

02:51 So let me, this is actually 1, okay? we have to reduce it from the matrix to one line, all right? so we can essentially let it be like this...

Question

Determine the value(s) of $x$ such that $[x \ 2 \ 1] \begin{bmatrix} 2 & 3 & -2 \\ 3 & 3 & 1 \\ -2 & -27 & 1 \end{bmatrix} \begin{bmatrix} x \\ -1 \\ -4 \end{bmatrix} = [0]$ $x = $ Note: If there is more than one value separate them by commas.

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