Determine , if possible , the value of x which will male the following true: begin{bmatrix}4 & 3 1 & x end{bmatrix}+2begin{bmatrix}2 1 end{bmatrix}begin{bmatrix}3 & x end{bmatrix}=begin{bmatrix}16 & 11 7 & 6 end{bmatrix}

sodni3 2021-03-18 Answered
Determine , if possible , the value of x which will male the following true:
[431x]+2[21][3x]=[161176]
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Expert Answer

Daphne Broadhurst
Answered 2021-03-19 Author has 109 answers
Step 1
Product of two matrices:
[ab][cd]=[abadbcbd]
Product of a scalar and a matrix:
k[abcd]=[kakbkckd]
If two matrices are equal then the corresponding elements of the matrices are equal.
Step 2
Given matrix equation is:
[431x]+2[21][3x]=[161176]
We need to find the value of x.
First, we need to simplify the left-hand side of the equation, and then we have to compare the elements of the left-hand side matrix and the right-hand side matrix.
[431x]+2[2×32×x1×31×x]=[161176]
[431x]+2[62x3x]=[161176]
[431x]+[2(6)2(2x)2(3)2(x)]=[161176]
Step 3
Now,
[431x]+[124x62x]=[161176]
[4+123+4x1+6x+2x]=[161176]
[163+4x73x]=[161176]
On comparing both sides, we get
3+4x=11 and 3x=6
4x=113 and x=63
4x=8 and x=2
x=84 and x=2
x=2 and x=2
Step 4
Answer: The value of x is 2.
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Jeffrey Jordon
Answered 2022-01-24 Author has 2064 answers

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