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Question 1 of 4
Solve for 2A2A given that:
A=[6-141810]
Incorrect
A constant multiplied to a matrix is simply distributed to each of the elements.
Substitute matrix A to 2A and solve.
2A |
= |
2[6-141810] |
Substitute A |
|
|
= |
[2×62×-142×182×10] |
Distribute 2 |
|
|
= |
[12-283620] |
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Question 2 of 4
Solve for -12A given that:
A=[6-141810]
Incorrect
A constant multiplied to a matrix is simply distributed to each of the elements.
Substitute matrix A to -12A and solve.
-12A |
= |
-12[6-141810] |
Substitute A |
|
|
= |
[−12×6−12×−14−12×18−12×10] |
Distribute -12 |
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|
= |
[-37-9-5] |
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Question 3 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
[132]
rows(m)=1
columns(n)=3
[610031122]
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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|
[132]×[610031122] |
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|
= |
[((1⋅6)+(3⋅0)+(2⋅1))((1⋅1)+(3⋅3)+(2⋅2))((1⋅0)+(3⋅1)+(2⋅2))] |
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|
= |
[6+0+21+9+40+3+4] |
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|
= |
[8147] |
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Question 4 of 4
Solve
[26-271031]×[3-146]
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
[26-271031]
rows(m)=2
columns(n)=4
[3-146]
rows(m)=4
columns(n)=1
Since the number of columns in the first matrix (4) and the number of rows in the second matrix
(4) are equal, these two matrices can be multiplied
Next, proceed with multiplying the two matrices
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[26-271031]×[3-146] |
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|
= |
[(2⋅3)+(6⋅−1)+(−2⋅4)+(7⋅6)(1⋅3)+(0⋅−1)+(3⋅4)+(1⋅6)] |
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|
= |
[6+(-6)+(-8)+423+0+12+6] |
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|
= |
[3421] |