smc-617-10-Matrix to SE

MATRICES, FUR1 2019 VCAA 5 MC

`[(2, 2, 0, -2), (2, 0, -2, 0), (0, 2, 0, -2), (2, 2, -2, 0)][(v), (w), (x), (y)]=[(2), (6), (-8), (4)]`

Which one of the following systems of simultaneous linear equations best represents the matrix equation above?

A.	`2v + 2w - 2y`	`= 2`	B.	`2v + 2w - 2y`	`= 2`
	`2v - 2x`	`= 6`		`2v - 2x`	`= 6`
	`2v - 2y`	`= -8`		`2w - 2y`	`= -8`
	`2v + 2w`	`= 4`		`2v + 2w - 2x`	`= 4`

C.	`2v + 2w + 2y`	`= 2`	D.	`2v + 2w - 2y`	`= 2`
	`2v - 2x`	`= 6`		`2v - 2x`	`= 6`
	`2w - 2y`	`= -8`		`2w - 2y`	`= -8`
	`2v + 2w - 2x`	`= 4`		`2v + 2w + 2x`	`= 4`

E.	`2v + 2w - 2y`	`= 2`
	`2v - 2w`	`= 6`
	`2w - 2y`	`= -8`
	`2v + 2w - 2x`	`= 4`

Show Answers Only

`B`

Show Worked Solution

`text(Creating equations from the matrix:)`

`2v + 2w – 2y`	`= 2`
`2v – 2x`	`= 6`
`2w – 2y`	`= -8`
`2v + 2w – 2x`	`= 4`

`=> B`

MATRICES, FUR1 2009 VCAA 4 MC

The matrix equation `[[4,2,8],[2,0,3],[0,3,−1]][[x],[y],[z]]=[[7],[2],[6]]` can be used to solve the system of simultaneous linear equations

A.	`4x + 2y + 8z = 7`
	`2x + 3y = 2`
	`3x - y = 6`

B.	`4x + 2y + 8z = 7`
	`2x + 3y = 2`
	`3y - z = 6`

C.	`4x + 2y + 8z = 7`
	`2y + 3z = 2`
	`3x - z = 6`

D.	`4x + 2y + 8z = 7`
	`2x + 3z = 2`
	`3y - z = 6`

E.	`4x + 2y + 8z = 7`
	`2x + 3z = 2`
	`3x - z = 6`

Show Answers Only

`D`

Show Worked Solution

`text(Expanding the matrix equation,)`

`4x + 2y + 8z = 7`

`2x + 3z = 2`

`3y – z = 6`

`=> D`

MATRICES, FUR1 2010 VCAA 5 MC

A system of three simultaneous linear equations is written in matrix form as follows.

`[(1, – 2, 0), (1, 0, 3), (0, 2, – 1)] [(x), (y), (z)] = [(4), (11), (– 5)]`

One of the three linear equations is

A. `x - 2y + z = 4`

B. `x + y + 3z = 11`

C. `2x - y = – 5`

D. `x + 3z = 11`

E. `3y - z = – 5`

Show Answers Only

`D`

Show Worked Solution

`text(Expanding the matrix,)`

`x – 2y`	`= 4`
`x + 3z`	`= 11`
`2y – z`	`= – 5`

`=> D`

MATRICES, FUR1 2012 VCAA 9 MC

`[(3,4), (1,2)] × [(a),(3)] = [(6,3), (2,-1)] × [(2),(b)]`

Which set of equations below could be used to determine the values of `a` and `b` that are shown in the matrix equation above?

A. `a - b = 2`

`a + b = 0`

B. `a + b = -2`

`a - b = 0`

C. `a + b = 2`

`a - b = 0`

D. `a - b = 8`

`a + b = 2`

E. `a - b = 8`

`a + b = -2`

Show Answers Only

`B`

Show Worked Solution

`text(Finding the matrix product of both sides:)`

`[(3,4),(1,2)][(a),(3)] = [(6,3),(2,−1)][(2),(b)]`

♦ Mean mark 39%.

`3a + 12`	`= 12 + 3b`
`a – b`	`= 0\ \ …\ (1)`

`a + 6`	`= 4 – b`
`a + b`	`=−2\ \ …\ (2)`

`rArr B`