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Question 1 of 4
Incorrect
Multiplying Two Matrices
[abc]×[pqr]=ap+bq+cr
Two matrices can be multiplied only if the number of columns (n) in the first matrix is equal to the number of rows
(m) in the second matrix.
First, check the dimensions of each matrix
[1200-13010]
rows(m)=3
columns(n)=3
[341]
rows(m)=3
columns(n)=1
Since the number of columns in the first matrix (3) and the number of rows in the second matrix
(3) are equal, these two matrices can be multiplied
Next, proceed with multiplying the two matrices
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[1200-13010]×[341] |
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= |
[(1⋅3)+(2⋅4)+(0⋅1)(0⋅3)+(−1⋅4)+(3⋅1)(0⋅3)+(1⋅4)+(0⋅1)] |
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= |
[3+8+00+(-4)+30+4+0] |
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= |
[11-14] |
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Question 2 of 4
Solve
[4213-52]×[324145261]
Incorrect
Multiplying Two Matrices
[abc]×[pqr]=ap+bq+cr
Two matrices can be multiplied only if the number of columns (n) in the first matrix is equal to the number of rows
(m) in the second matrix.
First, check the dimensions of each matrix
[4213-52]
rows(m)=2
columns(n)=3
[324145261]
rows(m)=3
columns(n)=3
Since the number of columns in the first matrix (3) and the number of rows in the second matrix
(3) are equal, these two matrices can be multiplied
Next, proceed with multiplying the two matrices
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[4213-52]×[324145261] |
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= |
[(4⋅3)+(2⋅1)+(1⋅2)(4⋅2)+(2⋅4)+(1⋅6)(4⋅4)+(2⋅5)+(1⋅1)(3⋅3)+(−5⋅1)+(2⋅2)(3⋅2)+(−5⋅4)+(2⋅6)(3⋅4)+(−5⋅5)+(2⋅1)] |
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= |
[12+2+28+8+616+10+19+(-5)+46+(-20)+1212+(-25)+2] |
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= |
[1622278-2-11] |
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Question 3 of 4
Solve for 2xy, given that:
x=[3-15-2] y=[10-43]
Incorrect
Multiplying Two Matrices
[abc]×[pqr]=ap+bq+cr
Two matrices can be multiplied only if the number of columns (n) in the first matrix is equal to the number of rows
(m) in the second matrix.
First, check the dimensions of matrices x and y
[3-15-2]
rows(m)=2
columns(n)=2
[10-43]
rows(m)=2
columns(n)=2
Since the number of columns in the first matrix (2) and the number of rows in the second matrix
(2) are equal, these two matrices can be multiplied
Next, substitute the two matrices to 2xy and solve
2xy |
= |
2×[3-15-2]×[10-43] |
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= |
[6-210-4]×[10-43] |
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= |
[(6⋅1)+(−2⋅−4)(6⋅0)+(−2⋅3)(10⋅1)+(−4⋅−4)(10⋅0)+(−4⋅3)] |
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= |
[6+80+(-6)10+160+(-12)] |
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= |
[14-626-12] |
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Question 4 of 4
Solve for x(x+y), given that:
x=[3-15-2] y=[10-43]
Incorrect
Multiplying Two Matrices
[abc]×[pqr]=ap+bq+cr
Two matrices can be multiplied only if the number of columns (n) in the first matrix is equal to the number of rows
(m) in the second matrix.
Two matrices can be added only if their dimensions (m×n) are equal.
First, check the dimensions of matrices x and y
[3-15-2]
rows(m)=2
columns(n)=2
[10-43]
rows(m)=2
columns(n)=2
Since the number of columns in the first matrix (2) and the number of rows in the second matrix
(2) are equal, these two matrices can be multiplied
Also note that since their dimensions are equal, they can be added
Next, substitute the two matrices to x(x+y) and solve
x(x+y) |
= |
[3-15-2]×([3-15-2]+[10-43]) |
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= |
[3-15-2]×[3+1-1+05+(-4)-2+3] |
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= |
[3-15-2]×[4-111] |
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= |
[(3⋅4)+(−1⋅1)(3⋅−1)+(−1⋅1)(5⋅4)+(−2⋅1)(5⋅−1)+(−2⋅1)] |
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= |
[12+(-1)-3+(-1)20+(-2)-5+(-2)] |
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= |
[11-418-7] |