If A=begin{pmatrix}8 & 0 4 & -2 3&6 end{pmatrix} text{ and } B=begin{pmatrix}2 & -2 4 & 2 -5&1 end{pmatrix} ,then find the matrix X such that 2A+3X=5B

Ava-May Nelson

Ava-May Nelson

Answered question

2021-02-02

If A=(804236) and B=(224251) ,then find the matrix X such that 2A+3X=5B

Answer & Explanation

Theodore Schwartz

Theodore Schwartz

Skilled2021-02-03Added 99 answers

Step 1
We have to find the matrix X such that 2A+3X=5B where matrices are given as: A=(804236) and B=(224251)
Here we have to use operation of matrices, in operation of matrices we focus on corresponding elements of the matrix.
Example:
2(abcd)=(2a2b2c2d),12(abcd)=(a2b2c2d2)
for addition of two matrices,
(abcd)+(xyzw)=(a+xb+yc+zd+w)
Step 2
Putting given value of matrices into the expression, we get
2A+3X=5B
2(804236)+3X=5(224251)
(2×82×02×42(2)2×32×6)+3X=(5×25(2)5×45×25(5)5×1)
(16084612)+3X=(10102010255)
3X=(10102010255)(16084612)
=(101610020810+4256512)
3X=(6101214317)
X=13(6101214317)
X=(6310312314331373)
=(2103414331373)
Hence, X=(2103414331373)

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